I'll plug The University of Texas, specifically the Natural Sciences and Liberal Arts colleges (COLA and CONS). This is because they used to be the same college, and as such have loads of slots for elective courses and often you'll find students from one taking classes in the other college.

I was able to complete degrees in COLA and a CONS simultaneously in four years with one of those four years being study abroad studying one subject to the exclusion of everything else because of it. When I graduated, I had studied two foreign languages and taken elective/upper div courses in poetry, immigration policy, ethics, mathematics, and computer science.

Unless things have drastically changed since I graduated, it still holds true for UT in particular, and is one reason I consider my education to have been so great.

Definitely. This, plus a graduate degree in a more specific field, and you end up with a very well-rounded education.