I think it's useful to bear in mind the nature of the potential interactions. Suppose you settle on a particular E and A in combination with some D and G. If you go changing the D and G, you will likely find that the responses of your E and A have changed. That makes sense when you consider how swapping strings can change the load on the top.
As Eric suggests, play around and find out. Personally, I've never been happy with a mixed set. I place a premium on a consistent overall sound and feel string-to-string. To each his own.
I agree with MrSidecar. In fact, I'd have Doms on my bass right now if it weren't for the breakage issue.