Would General Relativity work if gravity were not an inverse square law?

Question

I understand that General Relativity explains gravity by framing it as a consequence of the curvature of spacetime rather than as a force. Does this theoretically guarantee that gravity must be an inverse square law? Would it be possible in a different hypothetical Universe to have gravity which is a different power law, e.g. inverse cube, while still obeying the rules of General Relativity?