I have a student who is a double major in Engineering and Music. It is challenging - because both majors are challenging with no overlap - but he enjoys it. One reason he chose Case is because it is very doable as a double major as the program is very defined and established. You study with a music teacher from CIM. Music Theory (4 semesters) can be taken at Case or CIM - if that fits your schedule better. Same class. Music History requirements and electives are typically taken at Case. Their Orchestra, Wind Ensemble and other smaller groups are all first rate. You will be playing with very talented musicians. Additionally, the CIM dorm is attached/next to some of the North Side freshman dorms. My S made several friends there that he still plays music with.
Case is highly regarded for Music Ed but I can’t really tell you as much about that program. You don’t make a distinction of which music program you are interested in.