While Stadler's current offerings run heavely to EMU/DMU trains they have a section on their web site that says they will build any "cumstomised' train carrage you want. Obversiously the kicker here is the price, custom anything tends to be more expensive.
Of Stadler's normal product line the very multi capable FLIRT series would seem to suit at least some of Amtrak's requirement. With a seperate "power" carrage within the train they can offer O/H electric AC 25KV/50/60 Hz, 15k/11kV 16.66 Hz, DC 3,000/1,500V, third rail DC electric from 500 to 1200V [minimum] desiel and multi mode electric/desial. I don't know the maximum power of the desiel engines they can take.
I could see FLIRTS handling the Empire corridor with ease [& even through running with LIRR, if that actually happens as both under & over running third rail shoes could be fitted to the power module] as well as most of the NEC to unelectrified duties.
Slightly off topic: I recently saw a video on the "River Line" in NJ. That certainly look like a straight desiel FLIR, was it?