SQ flies FRA-JFK and back but it is on their oldest 747. But you will need a third party site or a TA to book this if you also want to include an LH flight to FRA from Italy.

Depending on your budget, the destination in the US and the time available you can take all sorts of crazy options TATL. TK via IST, MS via CAI, SK via CPH. But of course the best option is NZ via LHR which will be the best *A business class TATL.

But there is plenty of opportunity to try different things and see different cities as a nice stopover.