Joint accounts can have more than two members. You can also set up a joint account where transactions need two signatures for authorisation.
If an account is only in the name of the person for whom you were caring, the third party mandate stops when that person dies. This means you will not be able to withdraw money from the account. Even if the money has been left to you in a Will, you may still have to wait for probate to be granted to access the money.
If you have a joint account with the person for whom you are caring, you can continue to withdraw money after they die.