What follows is pure speculation and conjecture.
As noted in the previous post, astronomy suggests that dark matter ought to have a mass on the order of 1 keV to 13 keV, which is less than the mass of an electron and more than the likely mass of the neutrinos (there should be about one per cubic centimeter of space in our galaxy).
Yet, the evidence from weak force interactions is that all particles of less than 45 GeV (half the mass of a Z boson) are fully accounted for in the Standard Model, unless the W and Z bosons don't decay into them, violating the "democratic principle" that seems to apply to all other fundamental particles.
Dark matter ought to be stable and experience no significant decay. It ought to have a neutral electromagnetic charge.
But, there is really no experimental limitation that says that dark matter has to be a fundamental Standard Model particle. And, it would hardly be remarkable if a composite particle had a mass greater than the sum of its fermions, something that is generally true of every meson and baryon made of quarks. Indeed, more than 90% of the baryonic mass in the universe is attributable to the binding energy carried by gluons in protons and neutrons. Protons are stable, even in isolation, so it would hardly be surprising if some other particle could also be stable, even in isolation.
Imagine a force that only couples to fundamental particles that have neutral electromagnetic charge that is purely attractive with no repulsive component. It would be simpler than electromagnetism, or the weak force, or the strong force, or gravity in general relativity. Lacking electrical charge, photons would not interact with it. Lacking color charge, gluons would not interact with it.
This force would be strong, but wouldn't have to be confining or chiral, unlike the strong force. This force would operate only at short ranges, so the boson that carried it could be massive, perhaps on the same order of magnitude in mass as the W and Z bosons. Indeed, perhaps this boson, perhaps it could be called the X boson, could "eat" the fourth Higgs boson, just as the other three Higgs bosons are "eaten" by the W+, W- and Z bosons and eliminating the need for a fundamental particle with a spin of other than one or one-half. This would be in accord with electroweak fits for the Higgs boson suggested by LEP that put it at masses below that already excluded by collider experiments.
If an X boson had a mass very similar to that of the Z boson, the decays of the two electromagnetically neutral bosons might be indistinguishable in collider experiments.
I don't know precisely what this means in terms of group theory representations or the spin of the carrier boson, although I am tempted to imagine that it might correspond to the seemingly trival SU(1) or U(1) group, making for a neat SU(3) x SU(2) x SU(1) (or U(1)) x U(1) combination. This would leave four categories of bosons (photon, W/Z, gluon, and X), just as there are four categories of fermions (up, down, electron, neutrino). Alternately, perhaps it would be another manifestation of the weak force that would make the notion that the photon and Z boson are linear combinations of a W0 and B boson, as proposed by electroweak unification theory, unnecessary. They W0 could be the Z and the X could be the B.
The deficit of neutrinos that would arise from neutrinos binding into composite dark matter particles held together by X bosons would be negligible enough to escape notice in cosmological efforts to account for missing mass. Indeed, since the most recent census of baryonic matter suggests that it makes up closer to 50% of all non-dark energy in the universe, rather than the lion's share, and neither electrons or neutrinos in isolation make up much of the mass of the universe, composite neutrino dark matter bound by X bosons might mean that quarks and leptons would contribute roughly equal amounts to the total quantity of mass in the universe.
Since an electron neutrino and an electron antineutrino ought to annihilate if they were in close proximity, and hence would not be stable, composite neutrino dark matter might be made of either two electron neutrinos or two electron antineutrinos, which given the mass of the composite particle ought to make it possible to infer the coupling constant of the neutrino binding force carried by the X boson. Perhaps it would "coincidentally" be identical to the coupling constant of the Z boson with neutrinos. Indeed, perhaps the X boson equations would simply be a degenerate form of the equations that describe the W and Z bosons.
In this scenario, we would already have discovered all of the fundamental fermions and all but one of the fundamental bosons and there would be no free Higgs boson to discover, although we would be gaining one more fundamental force to the extent that it was not considered unified with the weak force. Since the weak force would cease to be even superficially unified with the electromagnetic force, the need for electroweak symmetry breaking through mechanism such as those found in supersymmetry and technicolor theories would be less necessary. There would be no need to have right handed sterile neutrinos either, since the composite ones could serve their role. Leptoquarks would also be unnecessary.
One of the problems with sterile neutrinos, particularly when there is just one kind of them, is where they fit in the Standard Model chart of fermions while remaining stable. If there is more than one generation of them, and they do not interact with the weak force, that presents its own issues. All other higher generation fermions are unstable and rapidly decay, and neutrinos oscillate incessantly. The odd keV sized composite dark matter particle would also be hard to distinguish experimentally from a plain old high energy neutrino.
One vaguely similar idea in the literature is found in this 2011 paper and here (also in 2011). The characteristic energy scale of the composite neutrinos in that model is also suggestively close at ca. 300 GeV to the vacuum expectation value of the Higgs field of 246 GeV.
Other non-neutrino composite dark matter proposals are found here and here and here.