Yes, Sasha, that is entirely possible!
Of course nothing prevents you from producing different breeds. I would view this more as the main breed type thing. Like if you have actual broodmares for an actual breeding program your character takes care of, that would count as a main breed. But if in your story you suddenly decide to breed that one Shetland pony mare just that one or two times in her lifetime, that wouldn't count as a main breed. If you see what I'm getting at.
It's kind of like the disciplines with the rider career. Yes they have to specialize in one, but if they enter local shows in another from time to time, that's fine. It works similarly in that regard. Now if you plan on breeding 2 breeds equally importantly but use the same characters for both, then yes I'd just put the career in both slots, one for each main breed.
And those are all great questions! As Christina mentioned somewhere, we are working on a newer better version of the ESRPG so presenting little "problems" like these are actually positive things because it helps us see what may need more explanation/improvement/complete redo.