Switching from Public Finance to ER or IB (or really any other part of finance)

I've been on the job search since August now. I am about to graduate with a finance degree in a couple months and I finally received a job offer. I have a lot of good intern experience, and I got this offer because I had an internship in public finance. This position is at a boutique municipal advisory firm working in derivatives. It seems like a cool position, however I do not know if public finance is for me. I have always had a long-term goal of working in research for equities. I obviously know these are not very related, but I don't have very many job prospects. Do you think it would be possible for me to switch from public finance into a different area like IB or ER in a couple years? I am also open and probably planning on getting MBA and/or CFA.