Hi, Tracy. This is difficult to tell without seeing it. What is under the old wainscotting? Plaster or wallboard from a prior renovation? Or is the wainscotting right to the studs?
In any case, putting wainscotting over wainscotting does not sound like a good approach. With the thickness, it will appear heavier than normal and be difficult to trim out.
Sorry I couldn't be more help.Henry in MI
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