Tire Advice for 1968 Barracuda
67 Barracuda, for what it's worth.
Rear with 255/60-15.
Front are 15x6, backspace 3.75, offset +6 mm with 215/65-15.
Judging by the clearances, uca, front and rear lower fender sections, I would guess a bigger diameter wheel would fit, but the offset would have to be larger and the height of the tire would probably have to be about the same.
Just a guess, those Barracuda fenders leave little room for steering.