diff --git a/src/dialect/mod.rs b/src/dialect/mod.rs
index 146ebf349..46e8dda2c 100644
--- a/src/dialect/mod.rs
+++ b/src/dialect/mod.rs
@@ -67,21 +67,29 @@ pub trait Dialect: Debug + Any {
     fn is_identifier_start(&self, ch: char) -> bool;
     /// Determine if a character is a valid unquoted identifier character
     fn is_identifier_part(&self, ch: char) -> bool;
-    /// Custom prefix parser
+    /// Dialect-specific prefix parser override
     fn parse_prefix(&self, _parser: &mut Parser) -> Option<Result<Expr, ParserError>> {
+        // return None to fall back to the default behavior
         None
     }
-    /// Custom infix parser
+    /// Dialect-specific infix parser override
     fn parse_infix(
         &self,
         _parser: &mut Parser,
         _expr: &Expr,
         _precendence: u8,
     ) -> Option<Result<Expr, ParserError>> {
+        // return None to fall back to the default behavior
         None
     }
-    /// Custom statement parser
+    /// Dialect-specific precedence override
+    fn get_next_precedence(&self, _parser: &Parser) -> Option<Result<u8, ParserError>> {
+        // return None to fall back to the default behavior
+        None
+    }
+    /// Dialect-specific statement parser override
     fn parse_statement(&self, _parser: &mut Parser) -> Option<Result<Statement, ParserError>> {
+        // return None to fall back to the default behavior
         None
     }
 }
diff --git a/src/parser.rs b/src/parser.rs
index a82c70400..5f1d2f145 100644
--- a/src/parser.rs
+++ b/src/parser.rs
@@ -1485,6 +1485,11 @@ impl<'a> Parser<'a> {
 
     /// Get the precedence of the next token
     pub fn get_next_precedence(&self) -> Result<u8, ParserError> {
+        // allow the dialect to override precedence logic
+        if let Some(precedence) = self.dialect.get_next_precedence(self) {
+            return precedence;
+        }
+
         let token = self.peek_token();
         debug!("get_next_precedence() {:?}", token);
         let token_0 = self.peek_nth_token(0);
@@ -4905,4 +4910,52 @@ mod tests {
             assert_eq!(ast.to_string(), sql.to_string());
         });
     }
+
+    #[test]
+    fn custom_infix_parser() -> Result<(), ParserError> {
+        #[derive(Debug)]
+        struct MyDialect {}
+
+        impl Dialect for MyDialect {
+            fn is_identifier_start(&self, ch: char) -> bool {
+                // See https://www.postgresql.org/docs/11/sql-syntax-lexical.html#SQL-SYNTAX-IDENTIFIERS
+                // We don't yet support identifiers beginning with "letters with
+                // diacritical marks and non-Latin letters"
+                ('a'..='z').contains(&ch) || ('A'..='Z').contains(&ch) || ch == '_'
+            }
+
+            fn is_identifier_part(&self, ch: char) -> bool {
+                ('a'..='z').contains(&ch)
+                    || ('A'..='Z').contains(&ch)
+                    || ('0'..='9').contains(&ch)
+                    || ch == '$'
+                    || ch == '_'
+            }
+
+            fn parse_infix(
+                &self,
+                parser: &mut Parser,
+                expr: &Expr,
+                _precendence: u8,
+            ) -> Option<Result<Expr, ParserError>> {
+                if parser.peek_token() == Token::Plus {
+                    assert!(parser.consume_token(&Token::Plus));
+                    Some(Ok(Expr::BinaryOp {
+                        left: Box::new(expr.clone()),
+                        op: BinaryOperator::Multiply, // translate Plus to Multiply
+                        right: Box::new(parser.parse_expr().unwrap()),
+                    }))
+                } else {
+                    None
+                }
+            }
+        }
+
+        let dialect = MyDialect {};
+        let sql = "SELECT 1 + 2";
+        let ast = Parser::parse_sql(&dialect, sql)?;
+        let query = &ast[0];
+        assert_eq!("SELECT 1 * 2", &format!("{}", query));
+        Ok(())
+    }
 }