Can you remove varnish with acetone?

Yes, acetone can be used to remove varnish. You must work on small areas at a time, as it evaporates quickly, in the direction of the wood grain. Also make sure to use lint free cloths when applying the acetone. Make sure you clean the surface well when you are done, as these solvents tend to leave residue behind. Then you can proceed to apply the varnish.