Intern at another company before starting job?

Hey,

I'm currently a college senior and was able to secure a job in consulting following an internship. Since they only gave me until a few weeks ago to accept the offer, I signed the contract given that I didn't have any alternatives at the time. However, I was also keen to apply for IB jobs at a few BB banks for next year, as that would be my preferred career path.

I understand that it could be damaging to apply for jobs in another industry and in turn renege on my consulting offer (or is this more common than I think?). But would it be feasible to at least apply for internships in between graduating and starting FT in consulting? If I were to receive a FT banking offer from an internship, I could always start after completing a couple of months in consulting...

There's the added complication that I'm graduating next year, so I'm not sure whether I'm eligible to apply for internships (which are usually aimed at juniors).

Does anyone have any ideas about how best to go about this?

Thanks!