You should be able to go into Settings > Get Paid, and click "Add Method" under the Payment Methods section to add another account. The same caveat as the first one applies, however. The account must be one that has your legal name on it, and you will have to verify that account as well.
One of the accounts will have to be chosen to be your "Preferred" account, but if you're manually withdrawing funds, you should be able to select which account you want to withdraw to.
Under no circumstances would I suggest trying to delete/add accounts back and forth, however. That would be a huge red flag. Just add the second one, verify them both, and use as necessary.
Please note that I am not a member of Upwork's staff, and as accurate as I try to be, there's always the possibility of me being wrong since I only have the same capabilities as you would.
