diff --git a/src/Psalm/Internal/Analyzer/Statements/ExpressionAnalyzer.php b/src/Psalm/Internal/Analyzer/Statements/ExpressionAnalyzer.php
index a7dda5a4f67..375f0e916ce 100644
--- a/src/Psalm/Internal/Analyzer/Statements/ExpressionAnalyzer.php
+++ b/src/Psalm/Internal/Analyzer/Statements/ExpressionAnalyzer.php
@@ -1311,23 +1311,54 @@ private static function fleshOutAtomicType(
                     return new Type\Atomic\TLiteralClassString($return_type->fq_classlike_name);
                 }
 
-                try {
-                    $class_constant = $codebase->classlikes->getConstantForClass(
-                        $return_type->fq_classlike_name,
-                        $return_type->const_name,
-                        \ReflectionProperty::IS_PRIVATE
-                    );
-                } catch (\Psalm\Exception\CircularReferenceException $e) {
-                    $class_constant = null;
+                if (strpos($return_type->const_name, '*') !== false) {
+                    $class_storage = $codebase->classlike_storage_provider->get($return_type->fq_classlike_name);
+
+                    $matching_constants = \array_keys($class_storage->class_constant_locations);
+
+                    $const_name_part = \substr($return_type->const_name, 0, -1);
+
+                    if ($const_name_part) {
+                        $matching_constants = \array_filter(
+                            $matching_constants,
+                            function ($constant_name) use ($const_name_part) {
+                                return $constant_name !== $const_name_part
+                                    && \strpos($constant_name, $const_name_part) === 0;
+                            }
+                        );
+                    }
+                } else {
+                    $matching_constants = [$return_type->const_name];
                 }
 
-                if ($class_constant) {
-                    if ($class_constant->isSingle()) {
-                        $class_constant = clone $class_constant;
+                $matching_constant_types = [];
+
+                foreach ($matching_constants as $matching_constant) {
+                    try {
+                        $class_constant = $codebase->classlikes->getConstantForClass(
+                            $return_type->fq_classlike_name,
+                            $matching_constant,
+                            \ReflectionProperty::IS_PRIVATE
+                        );
+                    } catch (\Psalm\Exception\CircularReferenceException $e) {
+                        $class_constant = null;
+                    }
+
+                    if ($class_constant) {
+                        if ($class_constant->isSingle()) {
+                            $class_constant = clone $class_constant;
 
-                        return array_values($class_constant->getAtomicTypes())[0];
+                            $matching_constant_types = \array_merge(
+                                \array_values($class_constant->getAtomicTypes()),
+                                $matching_constant_types
+                            );
+                        }
                     }
                 }
+
+                if ($matching_constant_types) {
+                    return $matching_constant_types;
+                }
             }
 
             return $return_type;
diff --git a/src/Psalm/Internal/Type/ParseTree.php b/src/Psalm/Internal/Type/ParseTree.php
index 6030bd6a64b..a300ba2165e 100644
--- a/src/Psalm/Internal/Type/ParseTree.php
+++ b/src/Psalm/Internal/Type/ParseTree.php
@@ -547,7 +547,7 @@ public static function createFromTokens(array $type_tokens)
                             $nexter_token = $i + 2 < $c ? $type_tokens[$i + 2] : null;
 
                             if (!$nexter_token
-                                || (!preg_match('/^[a-zA-Z_][a-zA-Z_0-9]*$/', $nexter_token[0])
+                                || (!preg_match('/^([a-zA-Z_][a-zA-Z_0-9]*\*?|\*)$/', $nexter_token[0])
                                     && strtolower($nexter_token[0]) !== 'class')
                             ) {
                                 throw new TypeParseTreeException(
diff --git a/src/Psalm/Internal/Visitor/SimpleNameResolver.php b/src/Psalm/Internal/Visitor/SimpleNameResolver.php
index 68f60a51290..f3ebec30c56 100644
--- a/src/Psalm/Internal/Visitor/SimpleNameResolver.php
+++ b/src/Psalm/Internal/Visitor/SimpleNameResolver.php
@@ -197,7 +197,7 @@ private function resolveType($node)
      * Resolve name, according to name resolver options.
      *
      * @param Name $name Function or constant name to resolve
-     * @param int  $type One of Stmt\Use_::TYPE_*
+     * @param Stmt\Use_::TYPE_*  $type One of Stmt\Use_::TYPE_*
      *
      * @return Name Resolved name, or original name with attribute
      */
diff --git a/tests/ConstantTest.php b/tests/ConstantTest.php
index f5c1aaf312f..25e99a2b4d6 100644
--- a/tests/ConstantTest.php
+++ b/tests/ConstantTest.php
@@ -622,6 +622,42 @@ class A {
                         public $foo = "a";
                     }',
             ],
+            'wildcardEnum' => [
+                '<?php
+                    class A {
+                        const C_1 = 1;
+                        const C_2 = 2;
+                        const C_3 = 3;
+
+                        /**
+                         * @param self::C_* $i
+                         */
+                        public static function foo(int $i) : void {}
+                    }
+
+                    A::foo(1);
+                    A::foo(2);
+                    A::foo(3);',
+            ],
+            'wildcardEnumAnyConstant' => [
+                '<?php
+                    class A {
+                        const C_1 = 1;
+                        const C_2 = 2;
+                        const C_3 = 3;
+                        const D_4 = 4;
+
+                        /**
+                         * @param self::* $i
+                         */
+                        public static function foo(int $i) : void {}
+                    }
+
+                    A::foo(1);
+                    A::foo(2);
+                    A::foo(3);
+                    A::foo(A::D_4);',
+            ],
         ];
     }
 
@@ -790,6 +826,23 @@ public static function bar(string $j) : void {}
                     A::bar("d");',
                 'error_message' => 'InvalidArgument',
             ],
+            'wildcardEnumBadValue' => [
+                '<?php
+                    class A {
+                        const C_1 = 1;
+                        const C_2 = 2;
+                        const C_3 = 3;
+                        const D_4 = 4;
+
+                        /**
+                         * @param self::C_* $i
+                         */
+                        public static function foo(int $i) : void {}
+                    }
+
+                    A::foo(A::D_4);',
+                'error_message' => 'InvalidArgument'
+            ],
         ];
     }
 }