Sometimes, and I do enjoy it.
It's much easier when when wearing a single statement piece is composed of mixed metals...which pulls together any additional pieces you throw on. Ex: the necklace above, Rolex watches, etc.
But it depends on the finishes and aesthetics. Pieces with similar aesthetics, as well as tarnished metals work more easily together. Also, gold+diamond pieces mix easier with silver and platinum because the diamond emits a cold, silvery glimmer.