diff --git a/CHANGELOG.md b/CHANGELOG.md
index 0240e4d5d9eb..bfb8b6e81e8b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -115,6 +115,7 @@ This release is compatible with NumPy 2.5.
 * Fixed `dpnp.nanmedian` dropping kept dimensions of size 1, which produced a wrong result shape [#3081](https://github.com/IntelPython/dpnp/pull/3081)
 * Fixed incorrect results of `dpnp.tensor.vecdot` in some cases with strided outputs and of `dpnp.tensor` reductions, `dpnp.tensor.vecdot` and `dpnp.tensor.matmul` on large inputs with some data types [#3082](https://github.com/IntelPython/dpnp/pull/3082)
 * Fixed `dpnp.median` and `dpnp.nanmedian` raising a `ValueError` for a tuple `axis` when a kept dimension has size 0 [#3081](https://github.com/IntelPython/dpnp/pull/3081)
+* Fixed a `RuntimeError` raised by `dpnp.tensor` kernels launched over more than `INT_MAX` work-items when built with DPC++ compiler 2026.2 or newer, by also passing `-fno-sycl-id-queries-fit-in-int` to the linker [#3089](https://github.com/IntelPython/dpnp/pull/3089)
 
 ### Security
 
diff --git a/dpnp/CMakeLists.txt b/dpnp/CMakeLists.txt
index e616e1964c56..5a93c42a6108 100644
--- a/dpnp/CMakeLists.txt
+++ b/dpnp/CMakeLists.txt
@@ -100,7 +100,10 @@ function(build_dpnp_tensor_ext _trgt _src _dest)
     if(BUILD_DPNP_TENSOR_SYCL)
         add_sycl_to_target(TARGET ${_trgt} SOURCES ${_generated_src})
         target_compile_options(${_trgt} PRIVATE -fno-sycl-id-queries-fit-in-int)
-        target_link_options(${_trgt} PRIVATE -fsycl-device-code-split=per_kernel)
+        target_link_options(
+            ${_trgt}
+            PRIVATE -fsycl-device-code-split=per_kernel -fno-sycl-id-queries-fit-in-int
+        )
         if(DPNP_TENSOR_OFFLOAD_COMPRESS)
             target_link_options(${_trgt} PRIVATE --offload-compress)
         endif()
diff --git a/dpnp/backend/extensions/indexing/CMakeLists.txt b/dpnp/backend/extensions/indexing/CMakeLists.txt
index 4242f053d1b5..e43d3d647529 100644
--- a/dpnp/backend/extensions/indexing/CMakeLists.txt
+++ b/dpnp/backend/extensions/indexing/CMakeLists.txt
@@ -96,7 +96,10 @@ else()
 endif()
 
 target_compile_options(${python_module_name} PUBLIC -fno-sycl-id-queries-fit-in-int)
-target_link_options(${python_module_name} PUBLIC -fsycl-device-code-split=per_kernel)
+target_link_options(
+    ${python_module_name}
+    PUBLIC -fsycl-device-code-split=per_kernel -fno-sycl-id-queries-fit-in-int
+)
 
 if(DPNP_GENERATE_COVERAGE)
     target_link_options(
diff --git a/dpnp/tensor/CMakeLists.txt b/dpnp/tensor/CMakeLists.txt
index 5345b672397d..67fa250ef630 100644
--- a/dpnp/tensor/CMakeLists.txt
+++ b/dpnp/tensor/CMakeLists.txt
@@ -346,7 +346,7 @@ foreach(python_module_name ${_py_trgts})
     )
     target_link_options(
         ${python_module_name}
-        PRIVATE -fsycl-device-code-split=per_kernel
+        PRIVATE -fsycl-device-code-split=per_kernel -fno-sycl-id-queries-fit-in-int
     )
     if(DPNP_TENSOR_OFFLOAD_COMPRESS)
         target_link_options(${python_module_name} PRIVATE --offload-compress)
diff --git a/dpnp/tests/third_party/cupy/binary_tests/test_packing.py b/dpnp/tests/third_party/cupy/binary_tests/test_packing.py
index 518e74d98868..6ffd64420d93 100644
--- a/dpnp/tests/third_party/cupy/binary_tests/test_packing.py
+++ b/dpnp/tests/third_party/cupy/binary_tests/test_packing.py
@@ -59,6 +59,24 @@ def test_pack_invalid_array(self):
         fa = cupy.array([10, 20, 30], dtype=float)
         pytest.raises(TypeError, cupy.packbits, fa)
 
+    @testing.slow
+    # @pytest.mark.thread_unsafe(reason="Allocation too large.")
+    @pytest.mark.parametrize(
+        "bitorder, expected", [("big", 128), ("little", 1)]
+    )
+    def test_packbits_large_input(self, bitorder, expected):
+        a = packed = None
+        try:
+            a = cupy.zeros(2**31 + 1, dtype=cupy.uint8)
+            a[-1] = 1
+            packed = cupy.packbits(a, bitorder=bitorder)
+            assert packed[-1] == expected
+        except MemoryError:
+            pytest.skip("out of memory in test.")
+        finally:
+            del packed, a
+            # cupy.get_default_memory_pool().free_all_blocks()
+
     def test_unpackbits(self):
         self.check_unpackbits([])
         self.check_unpackbits([0])
diff --git a/dpnp/tests/third_party/cupy/core_tests/test_ndarray_adv_indexing.py b/dpnp/tests/third_party/cupy/core_tests/test_ndarray_adv_indexing.py
index f4917393cd2a..53ae7f0ced6e 100644
--- a/dpnp/tests/third_party/cupy/core_tests/test_ndarray_adv_indexing.py
+++ b/dpnp/tests/third_party/cupy/core_tests/test_ndarray_adv_indexing.py
@@ -967,7 +967,12 @@ def test_adv_setitem_transp(self, xp):
 
 
 class TestHugeArrays:
-    # These tests require a lot of memory
+    # These tests use arrays with large logical sizes.
+    def test_take_negative_index_at_int32_size_boundary(self):
+        # Only the broadcast view is huge, so this needs no real allocation.
+        arr = cupy.broadcast_to(cupy.array(42, dtype=cupy.uint8), (2**31,))
+        assert arr.take(-1).item() == 42
+
     @testing.slow
     def test_advanced(self):
         try:
@@ -985,28 +990,41 @@ def test_advanced(self):
             pytest.skip("out of memory in test.")
 
     @testing.slow
+    # @pytest.mark.thread_unsafe(reason="Allocation too large.")
     def test_take_array(self):
+        arr = indices = res = None
         try:
-            arr = cupy.ones((1, 2**32), dtype=cupy.int8)
-            arr[0, 2**30] = 0  # We should see each of these once
-            arr[0, -1] = 0
-            res = arr.take(cupy.array([0, 0]), axis=0)
-            # sanity check, we mostly care about it not crashing.
-            assert res.sum() == 2 * (2**32 - 2)
+            arr = cupy.array([[[1, 2]], [[3, 4]]], dtype=cupy.uint8)
+            indices = cupy.broadcast_to(
+                cupy.array(0, dtype=cupy.int8), (2**30,)
+            )
+            res = arr.take(indices, axis=1)
+            testing.assert_array_equal(res[0, 0], [1, 2])
+            testing.assert_array_equal(res[0, -1], [1, 2])
+            testing.assert_array_equal(res[1, 0], [3, 4])
+            testing.assert_array_equal(res[1, -1], [3, 4])
         except MemoryError:
             pytest.skip("out of memory in test.")
+        finally:
+            del res, indices, arr
+            # cupy.get_default_memory_pool().free_all_blocks()
 
     @testing.slow
+    # @pytest.mark.thread_unsafe(reason="Allocation too large.")
     def test_take_scalar(self):
+        arr = res = None
         try:
-            arr = cupy.ones((1, 2**32), dtype=cupy.int8)
-            arr[0, 2**30] = 0  # We should see each of these once
-            arr[0, -1] = 0
-            res = arr.take(0, axis=0)
-            # sanity check, we mostly care about it not crashing.
-            assert res.sum() == 2**32 - 2
+            arr = cupy.broadcast_to(
+                cupy.array([[1], [2]], dtype=cupy.uint8), (2, 2**31)
+            )
+            res = arr.take(1, axis=0)
+            assert res[0] == 2
+            assert res[-1] == 2
         except MemoryError:
             pytest.skip("out of memory in test.")
+        finally:
+            del res, arr
+            # cupy.get_default_memory_pool().free_all_blocks()
 
     @testing.slow
     def test_choose(self):
diff --git a/dpnp/tests/third_party/cupy/creation_tests/test_basic.py b/dpnp/tests/third_party/cupy/creation_tests/test_basic.py
index 28f365026bff..4e42bc85e3e6 100644
--- a/dpnp/tests/third_party/cupy/creation_tests/test_basic.py
+++ b/dpnp/tests/third_party/cupy/creation_tests/test_basic.py
@@ -336,17 +336,17 @@ def test_full_like_subok(self):
 
     @pytest.mark.skip("_index_32_bits attribute is not supported by dpnp")
     @pytest.mark.slow
-    # thread_unsafe marker requires pytest-run-parallel, not used by dpnp
     # @pytest.mark.thread_unsafe(reason="large allocations")
     @pytest.mark.parametrize(
         "arr_factory,expected",
         [
             (lambda: cupy.empty(2**31 - 1, dtype=cupy.int8), True),
-            (lambda: cupy.empty(2**31, dtype=cupy.int8), True),
+            # Array sizes should fit as well, so 2**31 is also rejected:
+            (lambda: cupy.empty(2**31, dtype=cupy.int8), False),
             (lambda: cupy.empty(2**31 + 1, dtype=cupy.int8)[::2], False),
-            (lambda: cupy.empty(2**31 // 8, dtype=cupy.complex64), True),
+            (lambda: cupy.empty(2**31 // 8, dtype=cupy.complex64), False),
             (lambda: cupy.empty(2**31 // 8 + 1, dtype=cupy.complex64), False),
-            # Regression test for gh-9750:
+            # Regression test for gh-9750 (first view spans 2**31 - 4 bytes)
             (lambda: cupy.empty(2**31 // 8, dtype=cupy.complex64).real, True),
             (
                 lambda: cupy.empty(2**31 // 8 + 1, dtype=cupy.complex64).real,
diff --git a/dpnp/tests/third_party/cupy/creation_tests/test_matrix.py b/dpnp/tests/third_party/cupy/creation_tests/test_matrix.py
index 799ed954c70e..15441dc9ebbf 100644
--- a/dpnp/tests/third_party/cupy/creation_tests/test_matrix.py
+++ b/dpnp/tests/third_party/cupy/creation_tests/test_matrix.py
@@ -126,6 +126,39 @@ def test_tri_posi(self, xp, dtype):
         return xp.tri(*self.shape, k=1, dtype=dtype)
 
 
+class TestTriLargeDimensions(unittest.TestCase):
+
+    @testing.slow
+    # @pytest.mark.thread_unsafe(reason="Allocation too large.")
+    def test_large_number_of_rows(self):
+        out = None
+        try:
+            # k must be 0: a nonzero k lets a truncated 32-bit `row` wrap
+            # back onto the expected answer instead of failing.
+            out = cupy.tri(2**31 + 1, 1, k=0, dtype=cupy.uint8)
+            assert out[0, 0] == 1
+            assert out[-1, 0] == 1
+        except MemoryError:
+            pytest.skip("out of memory in test.")
+        finally:
+            del out
+            # cupy.get_default_memory_pool().free_all_blocks()
+
+    @testing.slow
+    # @pytest.mark.thread_unsafe(reason="Allocation too large.")
+    def test_large_number_of_columns(self):
+        out = None
+        try:
+            out = cupy.tri(1, 2**31, k=2**31 - 1, dtype=cupy.uint8)
+            assert out[0, 0] == 1
+            assert out[0, -1] == 1
+        except MemoryError:
+            pytest.skip("out of memory in test.")
+        finally:
+            del out
+            # cupy.get_default_memory_pool().free_all_blocks()
+
+
 @testing.parameterize(
     {"shape": (2,)},
     {"shape": (3, 3)},
diff --git a/dpnp/tests/third_party/cupy/random_tests/test_generator.py b/dpnp/tests/third_party/cupy/random_tests/test_generator.py
index 1cda3a3dc7cf..af33a006b52e 100644
--- a/dpnp/tests/third_party/cupy/random_tests/test_generator.py
+++ b/dpnp/tests/third_party/cupy/random_tests/test_generator.py
@@ -21,6 +21,15 @@
 pytest.skip("random.generator() is not supported yet", allow_module_level=True)
 
 
+def test_get_indices_preserves_uint64_cumsum_values():
+    sentinel = numpy.iinfo(numpy.uint64).max
+    csum = cupy.array([2**32 + 1, 2**32 + 1], dtype=cupy.uint64)
+    indices = cupy.full(2, sentinel, dtype=cupy.uint64)
+    _generator.RandomState._kernel_get_indices(csum, indices, size=csum.size)
+    assert indices[0] == 0
+    assert indices[1] == sentinel
+
+
 def numpy_cupy_equal_continuous_distribution(significance_level, name="xp"):
     """Decorator that tests the distributions of NumPy samples and CuPy ones.
 
diff --git a/dpnp/tests/third_party/cupy/random_tests/test_sample.py b/dpnp/tests/third_party/cupy/random_tests/test_sample.py
index b71ca1a43e7b..645d6a252ad5 100644
--- a/dpnp/tests/third_party/cupy/random_tests/test_sample.py
+++ b/dpnp/tests/third_party/cupy/random_tests/test_sample.py
@@ -7,6 +7,8 @@
 import dpnp as cupy
 from dpnp import random
 from dpnp.tests.third_party.cupy import testing
+
+# from cupy.random import _sample
 from dpnp.tests.third_party.cupy.testing import _condition, _hypothesis
 
 
@@ -293,6 +295,21 @@ def test_randn_invalid_argument(self):
 @pytest.mark.skip("random.multinomial() is not fully supported")
 class TestMultinomial(unittest.TestCase):
 
+    def test_kernel_accepts_large_n(self):
+        xs = cupy.array([0], dtype=cupy.int64)
+        ys = cupy.zeros(1, dtype="l")
+        _sample._multinominal_kernel(xs, 1, 2**31, ys)
+        assert ys[0] == 1
+
+    def test_kernel_uses_large_p_for_output_offset(self):
+        xs = cupy.array([0, 0], dtype=cupy.int64)
+        ys = cupy.zeros(2, dtype="l")
+        ys_view = cupy.lib.stride_tricks.as_strided(
+            ys, shape=(2, 2**31), strides=(ys.itemsize, 0)
+        )
+        _sample._multinominal_kernel(xs, 2**31, 1, ys_view)
+        testing.assert_array_equal(ys, cupy.ones(2, dtype="l"))
+
     @_condition.repeat(3, 10)
     @testing.for_float_dtypes()
     @testing.numpy_cupy_allclose(rtol=0.05)
diff --git a/dpnp/tests/third_party/cupy/statistics_tests/test_histogram.py b/dpnp/tests/third_party/cupy/statistics_tests/test_histogram.py
index edb713830e42..cfaeeecf55a3 100644
--- a/dpnp/tests/third_party/cupy/statistics_tests/test_histogram.py
+++ b/dpnp/tests/third_party/cupy/statistics_tests/test_histogram.py
@@ -8,6 +8,8 @@
 from dpnp.tests.helper import has_support_aspect64, numpy_version
 from dpnp.tests.third_party.cupy import testing
 
+# from cupy._statistics import histogram as histogram_module
+
 # Note that numpy.bincount does not support uint64 on 64-bit environment
 # as it casts an input array to intp (planned to support since 2.2.4).
 # And it does not support uint32, int64 and uint64 on 32-bit environment.
@@ -46,6 +48,43 @@ def for_all_dtypes_combination_bincount(names):
 
 class TestHistogram(unittest.TestCase):
 
+    # Number of bins that makes the searched index exceed 2**31.
+    _n_bins = 2**31 + 1
+
+    def _large_bins_and_counters(self, dtype):
+        # Equal bins send the binary search to the last one, `n_bins - 2`,
+        # without needing the gigabytes a monotonic `bins` would take. `y`
+        # only has to be indexable that far, and cycling it over three
+        # counters keeps it free while still recording which bin was picked.
+        bins = cupy.broadcast_to(
+            cupy.array([0], dtype=cupy.float32), (self._n_bins,)
+        )
+        counters = cupy.zeros(3, dtype=dtype)
+        y = cupy.lib.stride_tricks.as_strided(
+            counters,
+            shape=(self._n_bins // counters.size + 1, counters.size),
+            strides=(0, counters.itemsize),
+        )
+        return bins, counters, y
+
+    @pytest.mark.skip("_histogram_kernel is not supported")
+    def test_kernel_accepts_large_number_of_bins(self):
+        x = cupy.zeros(1, dtype=cupy.float32)
+        bins, counters, y = self._large_bins_and_counters(cupy.int64)
+        histogram_module._histogram_kernel(x, bins, bins.size, y)
+        # (2**31 - 1) % 3 == 1
+        testing.assert_array_equal(counters, [0, 1, 0])
+
+    @pytest.mark.skip("_weighted_histogram_kernel is not supported")
+    def test_weighted_kernel_accepts_large_number_of_bins(self):
+        x = cupy.zeros(1, dtype=cupy.float32)
+        weights = cupy.full(1, 2, dtype=cupy.float32)
+        bins, counters, y = self._large_bins_and_counters(cupy.float32)
+        histogram_module._weighted_histogram_kernel(
+            x, bins, bins.size, weights, y
+        )
+        testing.assert_array_equal(counters, [0, 2, 0])
+
     @testing.for_all_dtypes(no_bool=True, no_complex=True)
     @testing.numpy_cupy_allclose(atol=1e-6, type_check=has_support_aspect64())
     def test_histogram(self, xp, dtype):
diff --git a/dpnp/tests/third_party/cupy/statistics_tests/test_order.py b/dpnp/tests/third_party/cupy/statistics_tests/test_order.py
index 97d464fa63f2..2b3d22f9e41c 100644
--- a/dpnp/tests/third_party/cupy/statistics_tests/test_order.py
+++ b/dpnp/tests/third_party/cupy/statistics_tests/test_order.py
@@ -11,6 +11,8 @@
 # from cupy import cuda
 from dpnp.tests.third_party.cupy import testing
 
+# from cupy._statistics import order as order_module
+
 _all_methods = (
     "inverted_cdf",
     # 'averaged_inverted_cdf',      # TODO(takagi) Not implemented
@@ -51,6 +53,17 @@ def for_all_methods(name="method"):
     return pytest.mark.parametrize(name, _all_methods)
 
 
+@pytest.mark.skip("_get_percentile_weightnening_kernel() is not supported")
+def test_percentile_kernel_accepts_large_dimensions():
+    indices = cupy.array([0], dtype=cupy.float64)
+    a = cupy.broadcast_to(cupy.array([1], dtype=cupy.float64), (2**31,))
+    out = cupy.empty(1, dtype=cupy.float64)
+    order_module._get_percentile_weightnening_kernel()(
+        indices, a, 0, a.size, out
+    )
+    assert out[0] == 1
+
+
 @pytest.mark.skip("dpnp.quantile() is not implemented yet")
 @testing.with_requires("numpy>=1.22.0rc1")
 class TestQuantile:
diff --git a/dpnp/tests/third_party/cupyx/scipy_tests/linalg_tests/test_decomp_lu.py b/dpnp/tests/third_party/cupyx/scipy_tests/linalg_tests/test_decomp_lu.py
index 440521419652..251a5c7a450d 100644
--- a/dpnp/tests/third_party/cupyx/scipy_tests/linalg_tests/test_decomp_lu.py
+++ b/dpnp/tests/third_party/cupyx/scipy_tests/linalg_tests/test_decomp_lu.py
@@ -9,6 +9,8 @@
 import dpnp as cupy
 from dpnp.tests.third_party.cupy import testing
 
+# from cupyx.scipy.linalg import _decomp_lu
+
 if cupy.tests.helper.is_scipy_available():
     import scipy.linalg
 
@@ -20,6 +22,35 @@
 )
 
 
+@pytest.mark.skip("_kernel_cupy_split_lu is not supported")
+def test_split_lu_kernel_accepts_large_dimensions():
+    large = 2**31
+    lu = cupy.lib.stride_tricks.as_strided(
+        cupy.array([2], dtype=cupy.float32), shape=(large, 1), strides=(0, 0)
+    )
+    lower = cupy.empty(1, dtype=cupy.float32)
+    upper = cupy.empty(1, dtype=cupy.float32)
+    _decomp_lu._kernel_cupy_split_lu(
+        lu, large, 1, 1, lower._c_contiguous, lower, upper, size=1
+    )
+    assert lower[0] == 1
+    assert upper[0] == 2
+
+
+@pytest.mark.skip("_kernel_cupy_laswp is not supported")
+def test_laswp_kernel_accepts_large_dimensions():
+    large = 2**31
+    pivots = cupy.array([0], dtype=cupy.int64)
+    a_base = cupy.array([3], dtype=cupy.float32)
+    a = cupy.lib.stride_tricks.as_strided(
+        a_base, shape=(large, 1), strides=(0, 0)
+    )
+    _decomp_lu._kernel_cupy_laswp(
+        large, 1, 0, 0, pivots, 1, a._c_contiguous, a, size=1
+    )
+    assert a_base[0] == 3
+
+
 @testing.parameterize(
     *testing.product(
         {