Since you must balance 9 emulsions (on average) for color, it is more critical to have one process for all. Agfa failed years ago with their own proprietary process when Fuji and Kodak were using the same processes.
B&W is quite different and allows a larger variety of emulsions to be used. Of course this becomes critical with 3 emulsions in some cases in one B&W product.
I remember reading some Jobo literature on the web that suggests not processing Kodak and Fuji together. Sure pro labs do it but they have huge tanks with probably a gallon of chemistry per tank. You are putting 300ml of chemistry in your Jobo or so- much different.
I understand the creative possibilities, but sometimes I think too many possibilities can be detrimental, IMO. I make a print that I think looks good, then I think, "well, if I had done this or that, my picture would have looked "better." I put better in quotations because in reality, my prints would have looked different. Not better or worse, just different. I probably convinced myself that less variables would be better just because I tend to think of all the stuff I could or should have done :D
Edit: I hope this post doesnt hijack the thread. :D