Doug's solution using the plaster screws is the best you're going to do if hoisting 4x8 boards over your head isn't an option. Because you do sometimes have to use many, many of these screws to get the plaster rekeyed, you'll want to skim coat over the ceiling in this area to cover them (you can use drywall compound). A quick-fix I've used over large areas I've patched in plaster is to put down a fairly even coat of drywall compound, then cover the area with a large piece of nylon window screening cut to fit. Then put more compound over the top of the screen and smooth. It's kind of like having a great big piece of fibreglass drywall tape. When dry, you may have to add a couple more surface coats to smooth and feather out the edges of the patch, but it will hold forever. Sand, prime and paint.
It's still a lot of overhead ladder work, though, so have the linament at hand... your shoulders will need it! Best of luck.