Removing diamonds from a 14 karat gold ring with acid
I think that asking a jeweler is the best thing to do because gold is not something to throw away. However talking about the chemical concern, sulfuric acid can't oxidize gold, if the base metal (you should specify where and how it is) is iron theoretically you will be able to dissolve it with sulfuric acid:
$$\ce{Fe + H2SO4 -&gt;FeSO4 + H2 ^}$$

Something similar can happen with copper and tin but I think that temperature of the acid is a determinant parameter for these reactions.

If the base metal is inside the alloy is quite unlikely that you can affect it because gold is not a porous material, so you can only interact with the superficial layer.