It doesn't, and there are a list of examples in this nearly identical question: Deriving Newton's Third Law from homogeneity of SpaceDeriving Newton's Third Law from homogeneity of Space
There are no examples of fundamental classical three body forces where the forces are contact forces and linear gravity/EM, because linear fields are two-body interactions. The most obvious non two-body force is in the strong nonlinear gravitational regime.
Other physical examples are things like nucleon-nucleon 3-body forces, which are unfortuately completely quantum.
