There is a behind the scenes experience available but I didn't do it. Not sure what all is available
Not sure about here, but i dont think so. There is a monkey sanctuary in Palm Harbor tho
There are some behind the scenes tour that get you a little closer to the animals however you're still not closer enough to touch the animals and none of these are with primates. If you're looking for hands on try Exotic Animal Experience. It's technically a petting zoo but they have primates as well as other exotic animals.
Of all the times I've been, I've never seen this option. All animals are enclosed on their habitat with no interaction with humans.
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