To get a usable CPL you'll need to take the CPL written and
a CPL checkride (Two checkrides if you want single and multi)
I've never understood why the ME licence wouldn't simply cover the SE side of things. Can anybody explain? I have a friend with a Yankee CPL, and can only ever hire multi engine aircraft when he's there. On his last trip to the USA he wasn't permitted to hire a C172, so they gave him a King Air instead!