VFD for single phase induction motor?

Is this possible? I have a customer, a glass artist, who uses several very nice but old glass grinding machines. There are only 4 speeds on these machines and he would really like more speeds. He has a newer machine with a VFD on it and asked me how he could get the same thing on his old machines. I told him he really needs to change motors to 3 phase. But he is loathe to do that. I can see why. First of all the motors are beautiful. Secondly they are protected from the water that splashes on them, being totally enclosed. They also run very smoothly, having a run cap and great plain bearings. I would want to keep these old machines original too. Anyway, is there any sort of practical way to feed a cap run single phase from some sort of variable frequency drive? Thanks, Eric