There are some spots to the east of Guitar Lake if you want to avoid the crowds or the crowds have taken every little flat spot around the lake. Just look around.
There are also some small Bivy sites at the trail junction where the JMT and Whitney Trail merge before going the final 1.9 miles up to the Summit. You can camp there if your tent isn't too big and you're okay camping at 13,300 feet (not everyone is).
Or just drop your extra gear at the trail junction and go to the summit with water and snacks needed. Make sure any food is in your bear canister. No bears up there, but at least one Marmot that will do a full search of your bag contents. ????
