Spring Internship after accepting Full-Time offer

Hello all,

I had a question regarding internships after accepting a full time offer. If you did an SA stint somewhere and received a FT offer but graduate in December (and the FT can't start you earlier ie start in July), could you take a Spring internship at a different firm, maybe even in a different sector of Finance, just to gain more experience and learn a bit more? Assuming the Spring internship firm knows that you would not be in the position to stay FT and are just there to help out for a few months.

Thanks a bunch!