Absolutely!  If you’re looking at it as a “have to” versus a “get to,” you’re in the wrong place.

Having run many successful internship programs for 20 full years, the biggest point of resistance in true growth I’ve observed is duration.  Schools will often require that you do a semester and get quite insistent that you do no more, and often quite less.  This robs the student BIG TIME.  Real life isn’t broken into semesters and it’s simply unfair to get inadequate training.  You deserve the most knowledge you can get and this is for your future!  Get greedy and take as much as you can!