As I understand, the evidence for dark matter is the observation of the gravitational dynamics of objects around the size of galaxies and above. They move in a way such that the equations imply there is more mass than what we can see. There has never been any direct observation of dark matter, and our theories tell us it cannot be composed of any elementary particles from the standard model. Furthermore, there is no observation which suggests that dark matter is unevenly distributed, that some galaxies consisting of roughly the same amount of normal matter have varying amounts of dark matter.
I wonder if therefore an alternative explanation for the phenomena is that we have the wrong dynamical equations for gravity. Just as Newtonian gravitation is a good approximation to general relativity at low masses/energies, perhaps general relativity is a good approximation to the true gravitational theory at sub-galactic distances. Maybe when distances become very large we start seeing that gravatational force is described by slightly different curves than what general relativity predicts.
Is there any good evidence speaking against this alternative approach?
The reason this question is different from the "possible duplicate" is that the other question asks if the source of the effect attributed to dark matter is parallel universes, rather than different dynamical laws. However, the answer there does mention these alternative gravitational theories.
I realize now that this is not a new idea, and I thank the commenters and answerers for pointing me to existing research. However, this part of StackExchange does not bill itself as an "experts only" forum, so I don't think the downvotes are fair. In mathematics for example, there is one forum for experts, and another for everyone. I'm an expert in something, but not astronomy. Thanks.