In all the physics I know forces are always between pairs of things. Gravity is between pairs of masses, so is electrostatic repulsion, so are the strong and weak forces as far as I understand them (which is not very far).
Are there any hypothetical forces that are defined between three or more things?
Maybe quarks are somehow an example since three of them come together to make a proton or a neutron. But I'm especially interested in large-scale forces.
Can there be one that's like gravity? For example, what if every three masses interact in a way that accelerates them in a direction within the plane they define and perpendicular to the direction of some centroid? If any two of the three masses are equal, this "force" would net zero by reading the triple in both directions, but if they are all different maybe not. What else in physics would that break?
Naively, this would be a way to explain a galaxy rotation curve. Split the galaxy into three pie slices, and reading clockwise give one slice an abundance of light elements and a deficit of heavy, the next slice a normal amount, and the next slice more heavy than light. Then if the atoms in the galaxy are treated as point masses they pull on each other in the same direction as the observed rotation with an acceleration determined by however we've defined the "force". Alternatively, let all the point masses be the same, and define the force so that it is larger when the distance between consecutive pairs in the triple is increasing, then it seems like the existing spiral structure gives the asymmetry needed. Basically as long as some triangles are more common than their mirror image, then the mirror triangles are more common when looking at the galaxy upside-down, so there can be a positive net acceleration on each of the three masses even when they are equal.