Are you talking about sheep or goats? This is the goat forum... Females are called Does and males are called Bucks. (less commonly, 'nannies' and 'billies', which will make most breeders eye-twitch in displeasure, lol). Sheep are ewes and rams.
The reason most people keep one dairy breed is because the more breeds you have, the more bucks you need to be able to produce purebred kids. If you have 2 alpine does and 2 saanen does, you need at least 2 bucks, one of each breed... and once you start keeping offspring of your bucks, you either need to exchange bucks regularly (can be harder than it seems to find disease free quality bucklings), or start breeding doelings back to their sire. This may work out well or not.

So then you keep 2 bucks to breed the daughters of the other one to... soon you have 4 bucks and only 6-8 does total.
If you don't plan on keeping a buck, that can be another headache... you could try to hormonally synchronize heats, otherwise you'll have to drive each doe to a buck every time they go into heat... which is never synchronous it seems, lol. Many bucks may be far away, and there is an obvious disease risk in using just any buck. The good thing about this is that you aren't stuck with the same buck every year - if you don't like his daughters, you can just find a different buck without having to own the buck.
OR, you could produce crossbreds, which isn't bad, but you will not command the same prices as purebred most likely. It all really depends on your goals and desires for your herd.