Do you mean: is it possible to make a pure metal like gold denser? The aswer is no - the densty of a material is a function its atomic weight and its lattice structure. Metals generally have a structure consisting of tiny amorphous "grains." You can change the grain structure through operations like cold forming (stamping) or heat treating, which can help grains bind together better and thus improve the strength or hardness of the metal. But the fundamental density of the material is unchanged.
Of course the best way to make gold stronger is to alloy it with other metals. That's why rings or other jewelry are usually made up of an alloy of gold and other metals like silver. A 12K ring is about 50% gold and and is much harder and stronger than an equivalent pure 24K gold ring.