I thought of reposting your thread from last year. Reading it again, it did go off topic a bit.
It comes down to what type of account you mean. Closing and opening credit cards might be detrimental. The same does not apply for (ordinary) savings accounts. What does come into play is how the account is handled.
You would need to pick a bank that allows multiple accounts where this problem would be low. Don't forget you can check your own Credit score
I know that Wells Fargo and Key Bank run your credit when you open a account. So make sure you choose a bank that doesnt check your credit to open a account and you should be fine
I know if u open and close to many real walk in banks where u have to go in and sign up. if u open to many of these it will put u bad in chexsystem and u wont be able to get any more bank accounts after that