Switch Race and Class during combat?

[acrosome]

Let's say I am (have played) Class A and have Class B in my hand. I kick open the door and draw a monster who gets a bonus vs. Class A and a penalty vs. Class B.

You can discard a Race or Class card at any time.
You can play a new class or race card at any time on your own turn.

So, can I discard Class A and play Class B, and turn the monster's bonus into a penalty during combat?

Obviously, the same answer would apply to Race.