Many students do, but it is important to be realistic about the workload for each and how the deadlines mesh together. Moreover, make sure you get approval in advance from the registrar or advising staff at your primary institution for each course you want to transfer for credit.
Sometimes students think they can just take courses at multiple campuses and then apply them to a degree at a different institution later. This can be problematic. For example, an institution or a program may have a limit on the number of transfer credits they accept toward a degree or certificate. So a word to the wise: thoroughly review the admissions requirements and regulations for your destination school as early as possible.
Another issue is that students may only accept most types of financial aid from one institution at a time. Campuses may or may not have agreements to allow students to use aid from one campus at another one. Again, check with the financial aid officer at your primary campus.