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You bet! However, there does seem to be a tendency for "birds of a feather flock together" to occur. So getting 5 white birds (2 White Rocks, Delaware, White Orpington, White Ameraucana) and then a Speckled Sussex (or Polish or Salmon Faverolle) would likely put the Speckled Sussex as one that would be left out a bit and would likely be low on the pecking order which means that it could get "picked" on a bit. Chickens really do pay attention to which birds look like them. It makes a difference. So maybe make sure that there's at least two on any one color so each will have at least one friend. Meaning a Buckeye and a New Hampshire would probably see each other as close enough in color to run around together. You can still get six different breeds. But your may have a different experience. Social order dynamics are somewhat unpredictable since the number of variables can be so large.
Have fun with your chickens!