As an addendum, AA will happily check your bags through and protect you in case of a misconnect if everything is on the same ticket. However, to my knowledge no AA domestic fares are combinable with other carriers -- you can put together an itinerary with DL and AS segments for example because they both publish combinable fares, but not AA and AS.

The only way to currently connect from AA to AS on a (domestic, non-mileage) ticket is to buy a codeshare, and given that there are not currently codeshares on JFK-LAX or LAX-SFO, that is not currently possible.