Yes, you can go to a bank to change larger bills for smaller bills and coins. It's recommended you go to YOUR bank.
I have never seen them objecting to changing smaller bills to larger or larger to smaller, in MY bank. You just have to wait your turn for cashiers, and it may get a time consuming matter.
At least here in Higuey I have found out the best hour to viist a bank is about 2 pm (smallerst number of customers).