Like others have already mentioned, there are a few considerations when it comes to mixing species of tortoises. The main one, of course, is diseases which can be transmitted from one species who may have immunity to another species which does not have immunity. IF, and that is a big if, you can be absolutely certain all of the tortoises bein mixed are disease-free, then that problems becomes non-existent. A tortoise cannot transmit a disease it does not have.
Environment is a factor as well, but it is not much of a factor if you be sure to keep arid with arid, tropical with tropical, etc.
Another very real potential problem is that one species may be much more aggressive that another. A male tortoise that bites during courtship, like the desert tortoise does, can be very rough when he courts the female, and if he does this to a female of another species that does not have the tough skin on her front legs for protection, she may be badly injured. Some males also ram the female and others do not. If a rammer tries to court a female of another species who is not made for it, she can get injured that way as well.