Well, this one is tricky and don't understand how or why someone would just put a new coat of finish, over the existing. Most of the time, something like this just won't take. But let's assume it did. ...
Again. this is tricky but you could use some auto rubbing compound and you would really have to watch and control. You could also lightly rub with a product simular to WilBond but again, you really have to watch it. ....
This could get interesting and in the end, you may wind up just stripping it and refinishing. At any rate, please come back and let us know how you did and how you made out !!!
Good Luck and;
Be Safe !!!