The single most interesting feature of attempts to replace dark matter with a modification of gravity is Milgrom's discovery that in a wide variety of galaxies, there's a unique place where ordinary gravity plus ordinary matter stops working: when the acceleration due to gravity (as Newton would have calculated it) drops below a fixed value a0 ≈ 10^−10 m/s^2. This is the basis of MOND, but the pattern itself is arguably more interesting than any current attempt to account for it. Very possibly it can be explained by the complicated dynamics of baryons and dark matter in galaxies -- but in any event it should be explained somehow. The existence of this feature gives a strong motivation for testing gravity in the regime of very tiny accelerations. Note that this isn't even a statement that makes sense in general relativity; particles move on geodesics, and the "acceleration due to gravity" is always exactly zero. So implicitly we're imagining some global inertial frame with respect to which such acceleration can be measured. That's a job for a future theory to make sense of; for the moment we're forgetting that we know GR and thinking like Newton would have. So now Hernandez, Jimenez, and Allen have tried to test gravity in this weak-acceleration regime -- and they claim it fails!

The Breakdown of Classical Gravity? X. Hernandez, M. A. Jimenez, C. Allen Assuming Newton's gravity and GR to be valid at all scales, leads to the dark matter hypothesis as a forced requirement demanded by the observed dynamics and measured baryonic content at galactic and extra galactic scales. Alternatively, one can propose a contrasting scenario where gravity exhibits a change of regime at acceleration scales less than $a_{0}$, and obtain just as good a fit to observations across astrophysical scales. A critical experiment in this debate is offered by wide orbit binary stars. Since for $1 M_{odot}$ systems the acceleration drops below $a_{0}$ at scales of around 7000 AU, an statistical survey of relative velocities and binary separations reaching beyond $10^{4}$ AU should yield a conclusive answer to the above debate. By performing such a study we show Kepler's third law to fail precisely beyond $a approx a_{0}$ scales, precisely as predicted by modified gravity theories designed not to require any dark matter at galactic scales and beyond.

Color me dubious, but interested in seeing further studies. It's very hard to collect this kind of data, and note that it's just a statistical survey of velocities, not a precise measurement of individual systems. In principle a statistical survey is fine; in practice, it opens up the possibility of hidden subtle systematic effects. Still, intriguing and worth checking out. Any time you have the chance to overthrow Sir Isaac Newton, you go for it.