diff --git a/tests/IronPython.Tests/Cases/IronPythonCasesManifest.ini b/tests/IronPython.Tests/Cases/IronPythonCasesManifest.ini
index 28f12f138..aca492698 100644
--- a/tests/IronPython.Tests/Cases/IronPythonCasesManifest.ini
+++ b/tests/IronPython.Tests/Cases/IronPythonCasesManifest.ini
@@ -206,3 +206,6 @@ RunCondition=$(IS_POSIX) # Module resource is Posix-specific
 [IronPython.modules.system_related.test_sys_getframe]
 IsolationLevel=PROCESS # https://github.com/IronLanguages/ironpython3/issues/489
 FullFrames=true
+
+[IronPython.modules.system_related.test_sys]
+RunCondition=NOT $(IS_NETCOREAPP) # https://github.com/IronLanguages/ironpython3/issues/2057
diff --git a/tests/suite/test_array_stdlib.py b/tests/suite/test_array_stdlib.py
index 53ffd094d..3408e3b94 100644
--- a/tests/suite/test_array_stdlib.py
+++ b/tests/suite/test_array_stdlib.py
@@ -8,7 +8,7 @@
 
 import sys
 
-from iptest import is_ironpython, generate_suite, run_test
+from iptest import is_ironpython, generate_suite, run_test, is_posix
 
 import test.test_array
 
@@ -64,6 +64,10 @@ def load_tests(loader, standard_tests, pattern):
                 test.test_array.UnsignedShortTest('test_subclass_with_kwargs'), # https://github.com/IronLanguages/ironpython3/issues/767
                 test.test_array.UnsignedShortTest('test_type_error'), # https://github.com/IronLanguages/ironpython3/issues/767
             ]
+            if is_posix:
+                failing_tests += [
+                    test.test_array.LongTest('test_overflow'), # https://github.com/IronLanguages/ironpython3/issues/767
+                ]
 
         skip_tests = []
 
diff --git a/tests/suite/test_dict_stdlib.py b/tests/suite/test_dict_stdlib.py
index b1d4738eb..534f01580 100644
--- a/tests/suite/test_dict_stdlib.py
+++ b/tests/suite/test_dict_stdlib.py
@@ -31,6 +31,10 @@ def load_tests(loader, standard_tests, pattern):
             skip_tests += [
                 test.test_dict.DictTest('test_container_iterator'), # https://github.com/IronLanguages/ironpython3/issues/544
             ]
+            if sys.version_info >= (3, 6):
+                skip_tests += [
+                    test.test_dict.DictTest('test_free_after_iterating') # AssertionError
+                ]
 
         return generate_suite(tests, failing_tests, skip_tests)
 
diff --git a/tests/suite/test_socket_stdlib.py b/tests/suite/test_socket_stdlib.py
index 4754b7304..3be781002 100644
--- a/tests/suite/test_socket_stdlib.py
+++ b/tests/suite/test_socket_stdlib.py
@@ -46,7 +46,7 @@ def load_tests(loader, standard_tests, pattern):
                 failing_tests += [
                     test.test_socket.GeneralModuleTests('test_socket_fileno_requires_socket_fd'),
                 ]
-        if is_linux or (is_osx and net_version < (10, 0)):
+        if is_mono or sys.version_info < (3, 6) and (is_linux or (is_osx and net_version < (10, 0))):
             failing_tests += [
                 test.test_socket.NonBlockingTCPTests('testRecv'), # TODO: figure out
             ]
diff --git a/tests/suite/test_stdconsole.py b/tests/suite/test_stdconsole.py
index a40e9c6be..c70f4a97b 100644
--- a/tests/suite/test_stdconsole.py
+++ b/tests/suite/test_stdconsole.py
@@ -7,7 +7,7 @@
 import sys
 import unittest
 
-from iptest import IronPythonTestCase, is_cli, is_netcoreapp21, is_posix, run_test, skipUnlessIronPython
+from iptest import IronPythonTestCase, is_cli, is_netcoreapp21, is_posix, run_test, skipUnlessIronPython, is_netcoreapp
 
 if is_cli:
     import clr
@@ -404,7 +404,7 @@ def test_isatty(self):
         finally:
             self.batfile = hideDefaultBatch
 
-    @skipUnlessIronPython()
+    @unittest.skipIf(not is_cli or is_netcoreapp, "https://github.com/IronLanguages/ironpython3/issues/2057")
     def test_cp35263(self):
         script = """
 import warnings
diff --git a/tests/suite/test_types_stdlib.py b/tests/suite/test_types_stdlib.py
index 269eeafd0..f1e5ff2c7 100644
--- a/tests/suite/test_types_stdlib.py
+++ b/tests/suite/test_types_stdlib.py
@@ -8,7 +8,7 @@
 
 import sys
 
-from iptest import is_ironpython, generate_suite, run_test
+from iptest import is_ironpython, generate_suite, run_test, is_netcoreapp
 
 import test.test_types
 
@@ -28,12 +28,16 @@ def load_tests(loader, standard_tests, pattern):
         ]
         if sys.version_info >= (3, 6):
             failing_tests += [
-            test.test_types.ClassCreationTests('test_bad___prepare__'), # AssertionError
-            test.test_types.ClassCreationTests('test_one_argument_type'), # AssertionError: TypeError not raised
-            test.test_types.CoroutineTests('test_gen'), # https://github.com/IronLanguages/ironpython3/issues/98
-            test.test_types.CoroutineTests('test_genfunc'), # https://github.com/IronLanguages/ironpython3/issues/98
-            test.test_types.CoroutineTests('test_returning_itercoro'), # https://github.com/IronLanguages/ironpython3/issues/98
-        ]
+                test.test_types.ClassCreationTests('test_bad___prepare__'), # AssertionError
+                test.test_types.ClassCreationTests('test_one_argument_type'), # AssertionError: TypeError not raised
+                test.test_types.CoroutineTests('test_gen'), # https://github.com/IronLanguages/ironpython3/issues/98
+                test.test_types.CoroutineTests('test_genfunc'), # https://github.com/IronLanguages/ironpython3/issues/98
+                test.test_types.CoroutineTests('test_returning_itercoro'), # https://github.com/IronLanguages/ironpython3/issues/98
+            ]
+            if is_netcoreapp:
+                failing_tests += [
+                    test.test_types.CoroutineTests('test_duck_functional_gen'), # https://github.com/IronLanguages/ironpython3/issues/2054#issuecomment-4722599371 - TypeError: object of type 'str' can't be used in 'await' expression
+                ]
 
         skip_tests = []