I’m remodeling a 1970’s walk out basement. Both the above ground and below ground portions were originally framed with 2×2’s inside and tight to the cinder block walls.  R11 fiberglass batt was stuffed in the 1 1/2” depth walls. I’ve removed the fiberglass and have carefully fit extruded poly foam in the framed walls. I have access to additional 4×8 1/2” foam board at no cost.  My thought is to add one continuous & taped layer over the framing before hanging drywall next week to add more R value and provide a thermal break.  I would screw the drywall through the pretty dense layer into the 2×2 studs.

Is the benefit worth any challenges in finishing the drywall?  I’m in NW AR just into zone 4.