If you are in the Southern California area, you really should check out Sunrise Aviation at SNA. The instructor who does all the multiengine training is a retired Continental 777 Captain.

Any flight school will be happy to train with you full-time, if that's what you want to do. Especially if you want to do multi training. You don't have to go to ATP to train full-time. And their "fixed" price isn't really. You get an allotment of hours, and if you go over, you have to pay on an hourly basis, at hugely inflated prices. It says that specifically in the agreement you sign on your first day.