Maybe just solutions for non-Keplerian redshifts, see http://hyperphysics.phy-astr.gsu.edu/hbase/Astro/darmat.html second image and bracketing paragraphs.

As in computing, naming things is hard.

The redshifting things are mostly molecular gas clouds which we would expect would orbit in a Keplerian fashion given the overall distribution of luminous matter and occluding/extinguishing dust visible in galaxies. Astrophysicists love hydrogen gas clouds because they ionize easily from background emitters (stars, quasars) producing very sharp spectral lines, and you can pick up their changes by looking on different sides of an edge-on spiral or are at nearly perpendicular angles to the rotational axis of spheroidals. For giant ellipticals, which have practically zero axial rotation, an instrument that gets a sweeping view of them will see a more chaotic red-and-blue shifting of the Lyman-alpha hydrogen line, rather than an obvious gradient between advancing and retreating edges. (Face-on spirals often also have gas clouds on excursions back and forth in front of the disk plane, where "forth" means "towards us" means "relatively blueshifted" and that's hard to explain without a halo rather than a ring of dark matter).

So really it's a question explaining the non-Keplerian https://en.wikipedia.org/wiki/Peculiar_velocity of structures from ionized hydrogen to molecular clouds to supernovae with highly predictable light curves.

While basic MOND can explain edge-on spirals and axis-perpendicular spheroidals and lenticulars, it does a bad job with face-on spirals, ellipticals, and lots of other unusual shapes in the galaxy zoo. It also doesn't do well with entire clusters, where there are enormous gas clouds between the member galaxies, and often a bright quasar (or at least central galaxy) really lighting them up. Corrections to basic MOND patch some of these up, mostly starting by adding extra terms to the initial basic Milgrom formula which modified F = ma.

A ball-like distribution of dark matter around these very large structures (galaxies, clusters) on the other hand is a decent explanation, with the major drawback that the only sufficiently transparent stuff we've produced in labs is simply too light to stay constrained within these structures (electron neutrinos and their antis would fly away to infinity, for example, rather than stick around in a hierarchy of halo/shell/ball structures; free neutrons aren't stable). We also don't have a really good explanation about why these proposed dark matter structures don't have a strong density gradient leading to grossly non-Keplerian orbits of stars in the cores of galaxies (including our own). That's why you get wildly speculative ideas like phase transitions, "dark chemistry", dark-matter/dark-matter annihilation, and so on. There are similar questions about why the outer reaches of dark matter halos don't blow off into infinity rather than lingering around. ( See the excellent III A and III E of Adams & Laughlin https://arxiv.org/abs/astro-ph/9701131 or the Binney & Tremaine textbook https://press.princeton.edu/books/paperback/9780691130279/ga... )

Good explanations should cover the entire lifetime of a galaxy including the things that lead up to it and its ultimate decay. This also means it should be good for the oldest galaxies that we can see. It also means that as we get better at simulating initial value problems we can take a large number of observed quantities of a highly-redshifted galaxy and evolve that initial snapshot step by step such that after trillions of steps we end up with something that looks remarkably like a galaxy with low redshift. We're not really there yet. Work harder, supercomputer builders! :D :D