Definitely. You could add stone or wood to make it look like a full surround. I'm envisioning something like this white fireplace except without the natural wood or stone on the sides.

The second photo has wood just on the mantle and stone on the rest. I don't think you should cover up all that beautiful stone, but just adding sides in a soapstone or dark granite might be a really cool touch.

I don't know your budget, but if you would be okay parting with the existing mantel then perhaps my advice might work. I would try to find a longer piece of wood (hopefully in the same color) that can extend in both directions and match the ending of the rock. This will then allow you to add some height either through plants, candle sticks, etc. Something else to consider would be hanging pendants maybe in a cluster to the right or left of the mantle: two on one side, one on the other. Right now the dwarfed mantle is being swallowed by all the texture of the rock. If you give the mantle a bit more substance it'll help trick the eye.