Regarding increasing your miles (are you actually using miles, or are you on a Gold Challenge and using points?), that's easy. Connect through some AA hubs, like LAX, ORD, STL, MIA, IND, etc. As far as not increasing the price, we don't know your price, dates or fare basis, so that is hard to figure out.

And, do you want to keep the same refundability, or are you willing to take a nonrefundable fare in order to keep the same price and go a longer way?