Can I put plywood over the drywall on the common wall between my house and garage?
I think I am accurate in saying this.... As long as you keep the drywall layer at the house/garage, and do not damage it in any way (screws ok) you will not compromise the fire rating of the original sheetrock. The drywall at that wall is a requirement for fire safety, it is typically a thicker, 5/8", and fiberglass reinforced to withstand a potential fire in the garage for a time before it spreads to the house.