"Modified Newtonian dynamics (MOND) is a theory that proposes a modification of Newton's laws to account for observed properties of galaxies. It is an alternative to the theory of dark matter in terms of explaining why galaxies do not appear to obey the currently understood laws of physics." [1]
Seems like this is (one approach to) exactly the question I asked! Even if proven not to lead to any satisfactory cosmological model, these kind of studies will at least tell you why the alternatives (to r^2) don't hold.
