Most dealers make contact with similar financial sources that has a record of your credit score. Meaning if a bank has already made a decision regarding your loan application, transferring to another dealer will not change that decision. Banks base their decision of your credit score, not on your dealer. Automotive banks get annoyed reading similar applications from different sources. This will give them the impression that you are simultaneously getting multiple loans or even a fraudulent profile.
Even though lending institutions are the ones that dictating the terms and interest rates, working with a good lender that understands your situation and is interested in helping you secure a loan is a game changer. He or She might even make negotiations that will be beneficial to both parties.