diff --git a/.github/workflows/reusable_proxy_lib.yml b/.github/workflows/reusable_proxy_lib.yml
index 56211b97d..3c1903ff9 100644
--- a/.github/workflows/reusable_proxy_lib.yml
+++ b/.github/workflows/reusable_proxy_lib.yml
@@ -61,9 +61,14 @@ jobs:
 
       # TODO enable the provider_file_memory_ipc test when the IPC tests with the proxy library are fixed
       # see the issue: https://github.com/oneapi-src/unified-memory-framework/issues/864
+      # TODO enable the proxy_lib_basic test for the JEMALLOC proxy_lib_pool
+      # see the issue: https://github.com/oneapi-src/unified-memory-framework/issues/894
       - name: Run "ctest --output-on-failure" with proxy library
         working-directory: ${{env.BUILD_DIR}}
-        run: LD_PRELOAD=./lib/libumf_proxy.so ctest --output-on-failure -E provider_file_memory_ipc
+        run: >
+          LD_PRELOAD=./lib/libumf_proxy.so
+          ctest --output-on-failure
+          ${{ matrix.proxy_lib_pool == 'JEMALLOC' && '-E "provider_file_memory_ipc|proxy_lib_basic"' || '-E provider_file_memory_ipc' }}
 
       - name: Run "./test/umf_test-memoryPool" with proxy library
         working-directory: ${{env.BUILD_DIR}}
@@ -77,6 +82,18 @@ jobs:
         working-directory: ${{env.BUILD_DIR}}
         run: UMF_PROXY="page.disposition=shared-shm" LD_PRELOAD=./lib/libumf_proxy.so /usr/bin/date
 
+      # TODO enable the provider_file_memory_ipc test when the IPC tests with the proxy library are fixed
+      # see the issue: https://github.com/oneapi-src/unified-memory-framework/issues/864
+      # TODO enable the proxy_lib_basic test for the JEMALLOC proxy_lib_pool
+      # see the issue: https://github.com/oneapi-src/unified-memory-framework/issues/894
+      - name: Run "ctest --output-on-failure" with proxy library and size.threshold=128
+        working-directory: ${{env.BUILD_DIR}}
+        run: >
+          UMF_PROXY="size.threshold=128"
+          LD_PRELOAD=./lib/libumf_proxy.so
+          ctest --output-on-failure
+          ${{ matrix.proxy_lib_pool == 'JEMALLOC' && '-E "provider_file_memory_ipc|proxy_lib_basic"' || '-E provider_file_memory_ipc' }}
+
       - name: Check coverage
         if:  ${{ matrix.build_type == 'Debug' }}
         working-directory: ${{env.BUILD_DIR}}
diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt
index d24244ab0..54271d730 100644
--- a/test/CMakeLists.txt
+++ b/test/CMakeLists.txt
@@ -414,6 +414,9 @@ if(UMF_PROXY_LIB_ENABLED AND UMF_BUILD_SHARED_LIBRARY)
         SRCS ${BA_SOURCES_FOR_TEST} test_proxy_lib.cpp
         LIBS ${UMF_UTILS_FOR_TEST} umf_proxy)
 
+    set_property(TEST umf-proxy_lib_basic
+                 PROPERTY ENVIRONMENT "UMF_PROXY=size.threshold=64")
+
     # the memoryPool test run with the proxy library
     add_umf_test(
         NAME proxy_lib_memoryPool
diff --git a/test/test_proxy_lib.cpp b/test/test_proxy_lib.cpp
index 85afc65be..12f17ce5f 100644
--- a/test/test_proxy_lib.cpp
+++ b/test/test_proxy_lib.cpp
@@ -19,13 +19,14 @@
 
 using umf_test::test;
 
-#define SIZE_64 64
+// size threshold defined by the env variable UMF_PROXY="size.threshold=64"
+#define SIZE_THRESHOLD 64
+#define SIZE_EQ (SIZE_THRESHOLD)
+#define SIZE_LT (SIZE_THRESHOLD - 1)
+
 #define ALIGN_1024 1024
 
 TEST_F(test, proxyLib_basic) {
-
-    ::free(::malloc(SIZE_64));
-
     // a check to verify we are running the proxy library
     void *ptr = (void *)0x01;
 
@@ -41,46 +42,162 @@ TEST_F(test, proxyLib_basic) {
 }
 
 TEST_F(test, proxyLib_realloc_size0) {
-    // realloc(ptr, 0) == free (ptr)
+    // realloc(ptr, 0) == free(ptr)
     // realloc(ptr, 0) returns NULL
-    ASSERT_EQ(::realloc(::malloc(SIZE_64), 0), nullptr);
+    ASSERT_EQ(::realloc(::malloc(SIZE_EQ), 0), nullptr);
 }
 
-TEST_F(test, proxyLib_malloc_usable_size) {
-
-    void *ptr = ::malloc(SIZE_64);
-    ASSERT_NE(ptr, nullptr);
-    if (ptr == nullptr) {
-        // Fix for the following CodeQL's warning on Windows:
-        // 'ptr' could be '0': this does not adhere to the specification for the function '_msize'.
-        return;
-    }
+// The proxyLib_size_threshold_* tests test the size threshold of the proxy library.
+// The size threshold is set to SIZE_THRESHOLD bytes in this test, so all allocations of:
+// 1) size <  SIZE_THRESHOLD go through the default system allocator
+//    (umfPoolByPtr(ptr_size < SIZE_THRESHOLD) == nullptr)
+// 2) size >= SIZE_THRESHOLD go through the proxy library allocator
+//    (umfPoolByPtr(ptr_size >= SIZE_THRESHOLD) != nullptr)
 
+TEST_F(test, proxyLib_size_threshold_aligned_alloc) {
 #ifdef _WIN32
-    size_t size = _msize(ptr);
-#elif __APPLE__
-    size_t size = ::malloc_size(ptr);
+    void *ptr_LT = _aligned_malloc(SIZE_LT, ALIGN_1024);
+    void *ptr_EQ = _aligned_malloc(SIZE_EQ, ALIGN_1024);
 #else
-    size_t size = ::malloc_usable_size(ptr);
+    void *ptr_LT = ::aligned_alloc(ALIGN_1024, SIZE_LT);
+    void *ptr_EQ = ::aligned_alloc(ALIGN_1024, SIZE_EQ);
 #endif
 
-    ASSERT_EQ((int)(size == 0 || size >= SIZE_64), 1);
+    ASSERT_NE(ptr_LT, nullptr);
+    ASSERT_NE(ptr_EQ, nullptr);
 
-    ::free(ptr);
-}
+    // verify alignment
+    ASSERT_EQ((int)(IS_ALIGNED((uintptr_t)ptr_LT, ALIGN_1024)), 1);
+    ASSERT_EQ((int)(IS_ALIGNED((uintptr_t)ptr_EQ, ALIGN_1024)), 1);
+
+#ifndef _WIN32 /* the size threshold works only on Linux for now */
+    // umfPoolByPtr(ptr_size_LT) == nullptr
+    ASSERT_EQ(umfPoolByPtr(ptr_LT), nullptr);
+#endif
+    // umfPoolByPtr(ptr_size_EQ) != nullptr
+    ASSERT_NE(umfPoolByPtr(ptr_EQ), nullptr);
 
-TEST_F(test, proxyLib_aligned_alloc) {
 #ifdef _WIN32
-    void *ptr = _aligned_malloc(SIZE_64, ALIGN_1024);
+    _aligned_free(ptr_LT);
+    _aligned_free(ptr_EQ);
 #else
-    void *ptr = ::aligned_alloc(ALIGN_1024, SIZE_64);
+    ::free(ptr_LT);
+    ::free(ptr_EQ);
+#endif
+}
+
+TEST_F(test, proxyLib_size_threshold_malloc) {
+    void *ptr_LT = malloc(SIZE_LT);
+    void *ptr_EQ = malloc(SIZE_EQ);
+
+    ASSERT_NE(ptr_LT, nullptr);
+    ASSERT_NE(ptr_EQ, nullptr);
+
+#ifndef _WIN32 /* the size threshold works only on Linux for now */
+    // umfPoolByPtr(ptr_size_LT) == nullptr
+    ASSERT_EQ(umfPoolByPtr(ptr_LT), nullptr);
+#endif
+    // umfPoolByPtr(ptr_size_EQ) != nullptr
+    ASSERT_NE(umfPoolByPtr(ptr_EQ), nullptr);
+
+    ::free(ptr_LT);
+    ::free(ptr_EQ);
+}
+
+TEST_F(test, proxyLib_size_threshold_calloc) {
+    void *ptr_LT = calloc(SIZE_LT, 1);
+    void *ptr_EQ = calloc(SIZE_EQ, 1);
+
+    ASSERT_NE(ptr_LT, nullptr);
+    ASSERT_NE(ptr_EQ, nullptr);
+
+#ifndef _WIN32 /* the size threshold works only on Linux for now */
+    // umfPoolByPtr(ptr_size_LT) == nullptr
+    ASSERT_EQ(umfPoolByPtr(ptr_LT), nullptr);
+#endif
+    // umfPoolByPtr(ptr_size_EQ) != nullptr
+    ASSERT_NE(umfPoolByPtr(ptr_EQ), nullptr);
+
+    ::free(ptr_LT);
+    ::free(ptr_EQ);
+}
+
+TEST_F(test, proxyLib_size_threshold_realloc_up) {
+    void *ptr_LT = malloc(SIZE_LT);
+    void *ptr_EQ = malloc(SIZE_EQ);
+
+    ASSERT_NE(ptr_LT, nullptr);
+    ASSERT_NE(ptr_EQ, nullptr);
+
+    void *ptr_LT_r = realloc(ptr_LT, 2 * SIZE_LT);
+    void *ptr_EQ_r = realloc(ptr_EQ, 2 * SIZE_EQ);
+
+    ASSERT_NE(ptr_LT_r, nullptr);
+    ASSERT_NE(ptr_EQ_r, nullptr);
+
+#ifndef _WIN32 /* the size threshold works only on Linux for now */
+    // umfPoolByPtr(ptr_size_LT) == nullptr
+    ASSERT_EQ(umfPoolByPtr(ptr_LT_r), nullptr);
 #endif
+    // umfPoolByPtr(ptr_size_EQ) != nullptr
+    ASSERT_NE(umfPoolByPtr(ptr_EQ_r), nullptr);
 
-    ASSERT_EQ((int)(IS_ALIGNED((uintptr_t)ptr, ALIGN_1024)), 1);
+    ::free(ptr_LT_r);
+    ::free(ptr_EQ_r);
+}
+
+TEST_F(test, proxyLib_size_threshold_realloc_down) {
+    void *ptr_LT = malloc(SIZE_LT);
+    void *ptr_EQ = malloc(SIZE_EQ);
+
+    ASSERT_NE(ptr_LT, nullptr);
+    ASSERT_NE(ptr_EQ, nullptr);
+
+    void *ptr_LT_r = realloc(ptr_LT, SIZE_LT / 2);
+    void *ptr_EQ_r = realloc(ptr_EQ, SIZE_EQ / 2);
+
+    ASSERT_NE(ptr_LT_r, nullptr);
+    ASSERT_NE(ptr_EQ_r, nullptr);
+
+#ifndef _WIN32 /* the size threshold works only on Linux for now */
+    // umfPoolByPtr(ptr_size_LT) == nullptr
+    ASSERT_EQ(umfPoolByPtr(ptr_LT_r), nullptr);
+#endif
+    // umfPoolByPtr(ptr_size_EQ) != nullptr
+    ASSERT_NE(umfPoolByPtr(ptr_EQ_r), nullptr);
+
+    ::free(ptr_LT_r);
+    ::free(ptr_EQ_r);
+}
+
+TEST_F(test, proxyLib_size_threshold_malloc_usable_size) {
+
+    void *ptr_LT = ::malloc(SIZE_LT);
+    void *ptr_EQ = ::malloc(SIZE_EQ);
+
+    ASSERT_NE(ptr_LT, nullptr);
+    ASSERT_NE(ptr_EQ, nullptr);
+
+    if (ptr_LT == nullptr || ptr_EQ == nullptr) {
+        // Fix for the following CodeQL's warning on Windows:
+        // 'ptr' could be '0': this does not adhere to the specification for the function '_msize'.
+        return;
+    }
 
 #ifdef _WIN32
-    _aligned_free(ptr);
+    size_t size_LT = _msize(ptr_LT);
+    size_t size_EQ = _msize(ptr_EQ);
+#elif __APPLE__
+    size_t size_LT = ::malloc_size(ptr_LT);
+    size_t size_EQ = ::malloc_size(ptr_EQ);
 #else
-    ::free(ptr);
+    size_t size_LT = ::malloc_usable_size(ptr_LT);
+    size_t size_EQ = ::malloc_usable_size(ptr_EQ);
 #endif
+
+    ASSERT_EQ((int)(size_LT == 0 || size_LT >= SIZE_LT), 1);
+    ASSERT_EQ((int)(size_EQ == 0 || size_EQ >= SIZE_EQ), 1);
+
+    ::free(ptr_LT);
+    ::free(ptr_EQ);
 }