I'm somewhat of a purist, in that I don't think anyone should mix the species. I have at least a pair of every kind of American box turtle, and each species has their own outdoor pen.
I do keep all the different babies together, but when they're big enough to go outside, they are all separated by species.
I think just one male and female of every kind would get along peacefully as long as you don't mix them and you keep them in their own cage like emysemys said.
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they are right dont mix breeds and also watch out for the males and females together because they will fight because of mating trust me i have heard a lot of stories of males being mean to the females.
I've always kept Three Toed's with Eastern's for many, many years with no problems. I even had an Ornate for 32 years with them. Now I have a Gulf Coast in with some Three Toed's and Eastern's as well. I'm not going to sell any hatchlings, and I never took in any eggs (although I'm thinking of doing that soon) so I don't care if they breed together. The garden is big enough so that they get along, so far. I know that Tom over at TurtleTails keeps different species of Box Turtles together for years too, and I know of lots of friends who do the same, with no trouble. So I guess it's up to the individual, the size of your turtle garden, and if you are thinking of breeding to sell. If I was going to breed to sell, I would keep the line pure, and not mix species.
In this picture is an Ornate, Gulf Coast and a Eastern all eating together
in terms of american box turtles, there are different areas in nature where ranges for different turtles are thought to slightly overlap (for example, eastern and three toeds), so the mixing does happen in the wild a bit. i think the offspring of some of those overlap ranges have been seen on here esp. in terms of easterns and three toeds. (i have both and i've seen some on here that really do look like crosses.)
I have also kept Three Toeds and Easterns with no problems. Their territories overlap in the wild, and wild caught intergrades do occur.
Most people advise against keeping them together because they can and will interbreed. In the interests of keeping species pure, it is best not to let this happen, but if you intend to keep any offspring, and in the very least be completely honest about their origins in the even that you rehome any, I don't really see a big problem.
i don't mix species of boxers or subspecies though my baby Franklin lives with two grey tree frogs a green tree frog and an anole the greys are protected (inedable) but the green and anole could be eaten if he could catch them though unlike his sister he has never shown any interest in them.