diff --git a/sqlglot/parser.py b/sqlglot/parser.py
index 009573d910..50c242056f 100644
--- a/sqlglot/parser.py
+++ b/sqlglot/parser.py
@@ -4400,10 +4400,13 @@ def _parse_column_as_identifier() -> exp.Expr | None:
         return self._parse_wrapped_csv(_parse_column_as_identifier, optional=True)
 
     def _parse_join(
-        self, skip_join_token: bool = False, parse_bracket: bool = False
+        self,
+        skip_join_token: bool = False,
+        parse_bracket: bool = False,
+        alias_tokens: t.Collection[TokenType] | None = None,
     ) -> exp.Join | None:
         if self._match(TokenType.COMMA):
-            table = self._try_parse(self._parse_table)
+            table = self._try_parse(lambda: self._parse_table(alias_tokens=alias_tokens))
             cross_join = self.expression(exp.Join(this=table)) if table else None
 
             if cross_join and self.JOINS_HAVE_EQUAL_PRECEDENCE:
@@ -4430,10 +4433,12 @@ def _parse_join(
         if not skip_join_token and not join and not outer_apply and not cross_apply:
             return None
 
-        kwargs: dict[str, t.Any] = {"this": self._parse_table(parse_bracket=parse_bracket)}
+        kwargs: dict[str, t.Any] = {
+            "this": self._parse_table(parse_bracket=parse_bracket, alias_tokens=alias_tokens)
+        }
         if kind and kind.token_type == TokenType.ARRAY and self._match(TokenType.COMMA):
             kwargs["expressions"] = self._parse_csv(
-                lambda: self._parse_table(parse_bracket=parse_bracket)
+                lambda: self._parse_table(parse_bracket=parse_bracket, alias_tokens=alias_tokens)
             )
 
         if method:
@@ -4459,7 +4464,7 @@ def _parse_join(
             and not (kind and kind.token_type in (TokenType.CROSS, TokenType.ARRAY))
         ):
             index = self._index
-            joins: list | None = list(self._parse_joins())
+            joins: list | None = list(self._parse_joins(alias_tokens=alias_tokens))
 
             if joins and self._match(TokenType.ON):
                 kwargs["on"] = self._parse_disjunction()
@@ -4860,7 +4865,7 @@ def _parse_table(
             this.set("version", self._parse_version())
 
         if joins:
-            for join in self._parse_joins():
+            for join in self._parse_joins(alias_tokens=alias_tokens):
                 this.append("joins", join)
 
         if self._match_pair(TokenType.WITH, TokenType.ORDINALITY):
@@ -5056,8 +5061,10 @@ def _parse_pivots(self) -> list[exp.Pivot] | None:
             return None
         return list(iter(self._parse_pivot, None)) or None
 
-    def _parse_joins(self) -> t.Iterator[exp.Join]:
-        return iter(self._parse_join, None)
+    def _parse_joins(
+        self, alias_tokens: t.Collection[TokenType] | None = None
+    ) -> t.Iterator[exp.Join]:
+        return iter(lambda: self._parse_join(alias_tokens=alias_tokens), None)
 
     def _parse_unpivot_columns(self) -> exp.UnpivotColumns | None:
         if not self._match(TokenType.INTO):
diff --git a/sqlglot/parsers/clickhouse.py b/sqlglot/parsers/clickhouse.py
index 8d72bbfeeb..fbe22e4555 100644
--- a/sqlglot/parsers/clickhouse.py
+++ b/sqlglot/parsers/clickhouse.py
@@ -663,9 +663,14 @@ def _parse_join_parts(
         return is_global, side or kind, kind_pre or kind
 
     def _parse_join(
-        self, skip_join_token: bool = False, parse_bracket: bool = False
+        self,
+        skip_join_token: bool = False,
+        parse_bracket: bool = False,
+        alias_tokens: t.Collection[TokenType] | None = None,
     ) -> exp.Join | None:
-        join = super()._parse_join(skip_join_token=skip_join_token, parse_bracket=True)
+        join = super()._parse_join(
+            skip_join_token=skip_join_token, parse_bracket=True, alias_tokens=alias_tokens
+        )
         if join:
             method = join.args.get("method")
             join.set("method", None)
diff --git a/tests/dialects/test_mysql.py b/tests/dialects/test_mysql.py
index 3c9ac41ce2..b1eb4f455a 100644
--- a/tests/dialects/test_mysql.py
+++ b/tests/dialects/test_mysql.py
@@ -244,6 +244,13 @@ def test_ddl(self):
         self.validate_identity(
             "UPDATE foo JOIN bar ON TRUE SET foo.a = bar.a WHERE foo.id = bar.id"
         )
+        self.validate_identity(
+            "UPDATE items, month SET items.price = month.price WHERE items.id = month.id"
+        )
+        self.validate_identity("UPDATE a CROSS JOIN b SET a.x = 1")
+        self.validate_identity(
+            "UPDATE a, b LEFT JOIN c ON b.id = c.id SET a.x = 1, b.y = 2, c.z = 3"
+        )
 
         # PARTITION BY RANGE - simple column
         self.validate_identity(