2nd Fighting Style (lvl10) removes the 1st. The only way to keep the first is to go to the screen to choose the second, then go to previous screen and then go forward again to the choice screen. They will all then be there, so you can choose the one you had 1st. But doing this means you never get the second one that you should have.
I've tested this using the fighter. I'm unsure if this remains the case for any other class.
Also, this is using game v1.0.22 Final (from GoG)