Thanks for the effort but I found a work-around.
I didn't want to open both accounts at once. However, after booting, what even account I opened would be the ONLY one I could open even if using the other account name and password. This was the case using FireFox. So now, I use FireFox to open one of the accounts and later if needed, I can open the other account using MS Edge.
I think, FireFox is replacing my log in with the account information first used after boot.