diff --git a/reframe/core/pipeline.py b/reframe/core/pipeline.py
index 4748f00469..858bae8aac 100644
--- a/reframe/core/pipeline.py
+++ b/reframe/core/pipeline.py
@@ -158,7 +158,9 @@ class RegressionTest(metaclass=RegressionTestMeta):
                                             typ.List[str])
 
     #: List of systems supported by this test.
-    #: The general syntax for systems is ``<sysname>[:<partname]``.
+    #: The general syntax for systems is ``<sysname>[:<partname>]``.
+    #: Both <sysname> and <partname> accept the value ``*`` to mean any value.
+    #: ``*`` is an alias of ``*:*``
     #:
     #: :type: :class:`List[str]`
     #: :default: ``[]``
@@ -949,19 +951,16 @@ def info(self):
 
         return ret
 
-    def supports_system(self, partition_name):
-        if '*' in self.valid_systems:
-            return True
-
-        if self.current_system.name in self.valid_systems:
-            return True
+    def supports_system(self, name):
+        if name.find(':') != -1:
+            system, partition = name.split(':')
+        else:
+            system, partition = self.current_system.name, name
 
-        # Check if this is a relative name
-        if partition_name.find(':') == -1:
-            partition_name = '%s:%s' % (self.current_system.name,
-                                        partition_name)
+        valid_matches = ['*', '*:*', system, f'{system}:*',
+                         f'*:{partition}', f'{system}:{partition}']
 
-        return partition_name in self.valid_systems
+        return any(n in self.valid_systems for n in valid_matches)
 
     def supports_environ(self, env_name):
         if '*' in self.valid_prog_environs:
diff --git a/unittests/test_pipeline.py b/unittests/test_pipeline.py
index b5ce62c24f..e0c010921a 100644
--- a/unittests/test_pipeline.py
+++ b/unittests/test_pipeline.py
@@ -263,6 +263,12 @@ def test_supports_system(self):
         assert test.supports_system('testsys:gpu')
         assert test.supports_system('testsys:login')
 
+        test.valid_systems = ['*:*']
+        assert test.supports_system('gpu')
+        assert test.supports_system('login')
+        assert test.supports_system('testsys:gpu')
+        assert test.supports_system('testsys:login')
+
         test.valid_systems = ['testsys']
         assert test.supports_system('gpu')
         assert test.supports_system('login')
@@ -287,6 +293,17 @@ def test_supports_system(self):
         assert not test.supports_system('testsys:gpu')
         assert not test.supports_system('testsys:login')
 
+        test.valid_systems = ['*:gpu']
+        assert test.supports_system('testsys:gpu')
+        assert test.supports_system('foo:gpu')
+        assert not test.supports_system('testsys:cpu')
+        assert not test.supports_system('testsys:login')
+
+        test.valid_systems = ['testsys:*']
+        assert test.supports_system('testsys:login')
+        assert test.supports_system('gpu')
+        assert not test.supports_system('foo:gpu')
+
     def test_supports_environ(self):
         test = self.loader.load_from_file(
             'unittests/resources/checks/hellocheck.py')[0]