I know not enough physics to tell if this is reasonable but...
What if there's not just 4 base forces but 5, or an infinite class of them? Say something that falls off sub-quadratically but with a significantly lower constant than gravity? Or a whole class of forces that fall off less and less slowly, but have smaller and smaller constants as they do?
The forces, to be a useful modelling tool, need a medium to interact with matter. E.g. an equivalent of charge would always be zero, if matter didn't have the ability to have charge. At that point, it effectively doesn't exist.
Interestingly, the strong, weak and electromagnetic forces are also aspects of the same force. They unify at high enough energy levels. They only appear different. The exception is gravity. It doesn't fit the mould. Basically we don't currently have 4 forces, but only 2. Scientists suspect it's actually only 1, but can't yet unify gravity into a theory of everything via a theory of quantum gravity.
But isn't gravity a function of spacetime not matter? Where's the others are all behaviors of matter? Like there isn't a gravity partical or a spacetime partical.
Ultimately, physics follows the maths, everything else is interpretation to comprehend what the maths is telling us.
In relativity, gravity is a smooth, continuous distortion of spacetime. In QM, gravity is just another force, mediated by the graviton. Both theories are consistent with the known maths. The fact that they don't agree shows the large hole we have in the maths.
In short, we don't know what gravity is. Then again, we don't know what most things are, once we did deep enough. We just have maths, with interpretations that let our monkey brains make sense of them.
My favourite example ample of this is the "dark sucker theory". Envision a universe where light producing objects don't produce light, but suck up dark. We can make the model work for our universe. The reason we don't use it is due to it being harder to work with than the light emitter model. Another one is the rabit hole of what relativity says about the existence of light (hint light doesn't exist, from light's point of view).