Can you take CC classes while in university?

So I was wondering, is it possible if I take non-UC transferable classes at a community college while in university? For example, I take my general education classes at the university I attend and take non-UC-transferable classes in a community college. If taking non-UC-transferable classes is not allowed, am I able to take UC transferable classes while in university?

You would have to check with UCSC. What would be the purpose and do you plan to take these classes during the school year or summer? During the school year, you will have a full schedule to try in fit in these extra classes.