Have worked with hundreds of merchant accounts and across dozens of companies. It's standard practice to have multiple, redundant payment processors and merchant accounts in some industries and even traditional ecommerce when volumes are high enough.
Only if there is an exclusivity clause in their agreement and only if they enforce that clause, so double check the terms and conditions. I have seen some sneaky PSPs try to make merchants sign agreements with exclusivity.
Under card scheme (Visa, Mastercard, and so on) regulations, you are allowed︀ to have multiple merchant accounts.