Like peter I too had a limited US ATP issued on the basis of a European license but decided that I wanted a proper back up. I had a question/answer book airfreighted which covered dispatchers, choppers, jets and prop aircraft licences and read through it twice not realising that there were only certain sections revalent. I flew to Vegas, flew a twin over a week including a day trip to Phoenix to take my theory test and on the 8th day did my flight test. A few years later I added a sailplane commercial although I’ve never needed to use either license.
Found the theory exceptionally easy compared with my European written but then again I’d been flying for nearly two decades. Good luck.