a second camera is really nice if you are doing weddings or beach photography (avoid changing lens in the salt air/sand)
there are a few other instances of where getting a second camera would be nice. But there is overwhelming instances of where a nice lens that would advance your photography would be a much better choice.
You can continue to use your big zoom for wildlife and such, since a primo big zoom is out of your budget.
But a nice, very nice wide angle or longer portrait lens prime is within your budget. You could add either a 35mm 1.4 or a 85mm 1.4 Samyang/Rokinon lens and you would absolutely LOVE it. They are manual focus but the glass is so sweet you won't mind.
I have many cameras, including the T3i, 50D, 5Dc, 5D Mk II, and others and I would suggest that going with better lens is the best option, but if you insist on the second camera then a full frame would be a nice alternative, and the 5Dc is one heck of a nice portrait camera. AF isn't the greatest, but for slow moving or posed subjects, it gives one nice looking image.


