I was just thinking about how in our universe the orbital speeds of stars in the outer parts of galaxies are faster than they should be based on the visible matter in galaxies because galaxies have more dark matter than visible matter and the amount of matter in the galaxy slows down the drop off rate of gravity in the galaxy. In a solar system the drop off rate for gravity is r-2 because we live in three dimensions and because most of the mass of a solar system is concentrated in the star. If most of the mass of a solar system were outside the star then depending on how much mass was outside the star gravity could drop off at a slower rate than the inverse square law within the solar system even in four spatial dimensions.
In any number of dimensions if there is a hypersphere with uniform density gravity will increase linearly with distance from the center within the hypersphere. If most of the mass of a 4d solar system was in the form of dark matter outside the star then the drop off rate for gravity in the solar system could be slower than the inverse cube law which could help planets stay in stable orbits without having to come up with some weird force law.