I have learned that MOND can be obtained from a potential that adds a logarithmic potential to the usual inverse-square potential, with the logarithmic potential dominating past a certain distance, and producing a 1/r force law.
Also, while researching the history of neutrino theories of gravity (!), I ran across Chapter 2 of Feynman's rare "Lectures on Gravitation", in which he considers a peculiar three-way interaction, between two bodies and large distant masses, which produces a potential with a dominant logarithmic term (see equation 2.4.6).
Could something like this give us MOND?!
