this is simple,
you have to study the IR and the CPL theory (2 big big books you can buy online). when in the USA(when u are on vacation), find a free lance CFI in a small airport , do some hours on a light twin ( 150$/h ), and he will sign you off for the written exams(much harder than the ATPL, fully pass or fully fail and mainly based on experience and not stupid theory from the CAA ) , and the IR-multi check ride.
and u need a FAA first class medical, 70-80$ for a 30 minutes visit, harder than the JAA one, they look if you can fly, not if you can open your wallet)
and get the FARAIM from the FAA.gov website, and forget all the JAA **** you have learned in Europe...