using the scrabble blank tiles in the same game

As far as I am aware, the owner of a blank tile can use it as any letter he or she so chooses.

Your description seems a bit confusing. Do I have the scenario right?

Once a blank tile is placed on the board and is assigned as, let's say, a letter 'E', then for the duration of the game it maintains that identity.

Furthermore, any second blank tile placed can be whatever letter you want to assign to it, regardless of however many blanks there are on the board.

What the others said.