Well if we want to revive the Hereford breed purity thread....
My cattle are mutts... The most crossed up ones are 6 breeds, the least are about 3 breeds.
I'm going to refer you to any of DocHarris's posts about selection, I think he makes it pretty clear... He usually says something along the lines of "the breed is unimportant, as long as you are consistent in the multiple traits you're selecting for and they're balanced.
Our selection was a bit hodge-podge our first 10 or 15 years, but we did always get quality bulls.. So by hook or by crook, our herd still got better... I think we've improved it enough now that further improvements will need to be explicit and deliberate.
I think a lot of the fuss about too many breeds in an animal are a little exaggerated.. If you use purebred bulls consistently, the relevance of a breed 5 generations back is going to be pretty small.. If you've selected for quality animals, I don't see a big deal with it in a commercial environment... If you're using mongrel bulls on mongrel cows, you can have 8 breeds in only 2 generations, each one contributing 12.5%, as opposed to a decreasing scale of 50%, 25%, 12.5%, 6.25%, and finally the fifth breed would only be 3% if you used PB bulls... Not much to be concerned about there.