Is there a way to add more than one type hinting to a method? For example, foo(param) must receive a instance of string OR bar OR baz.
That is not possible to enforce (except inside the method). You can only provide a single type hint, and only to objects/interfaces and arrays (since PHP 5.1).
You can/should however document it in your method, i.e:
/**
* @param string|Bar|Baz $param1
*/
function foo($param1);