Yes, abdominoplasty can be done under anesthesia other than general, but why? It is a large and involved procedure. It involves tissue supplied by multiple nerves so the area is hard to anesthetize well safely. In this case, general anesthesia is probably safer. One reason some surgeons use local anesthesia is that they do not have privileges at a facility where general anesthesia can be used. Therefore, always ask if the surgeon has privileges to do the procedure in a certified facility. If not, be very wary. The other question is why not do a muscle repair. Almost everyone who needs an abdominoplasty also needs the muscle (actually the covering layer, or fascia) tightened. The same forces that stretched the skin generally stretch the muscle fascia. This is so, even if you have good muscle strength. When the muscles relax, they separate if the fascia is lax. Therefore, almost everyone needs this tightened.