general relativity - Could there be a "massive gravity" theory?

If we talk about a "quantum theory" of General Relativity, we know that the particle that mediates the gravitational force would be the so called Graviton, a massless particle with spin $2$.

I wonder if (and if it would work) there could be also a different theory like a "massive gravity", whose force is mediated by a massive boson (maybe not that massive too, even a small mass). What would it implicate?