Im wondering if it's possible to change the invincibility during certain attacks.

I have my dodges set up as separate moves. I also added a variable to the hitType - Horizontal, Vertical  Basically, I was wondering if it was possible to make it so while the character is dodging, vertical attacks don't hit, but horizontal attacks do.

This is the system certain Soul Calibur games use.

The dodge Move would probably need  a new type of invincibility, Dodge Invincibility, that is only works, as stated, on vertical attacks, whereas horizontal attacks still land a hit.