Though they are three separate species, they not only can crossbreed, they already have. All of the platies, swordtails, and variatus in the trade (except for the occasional rare import of wild fish) are technically hybrids. They have been crossed with each other to introduce traits, such as color and fin length, to the other species. So none of the three are 100% pure.
But, having said that, the fish will preferentially mate with their own species and usually ignore the other species, unless mates of their own kind are missing. Usually. But as Kevin pointed out, there are some gold gouramies out there that are irresistibly hot!
