As the early efforts to use the GAMBIT software that fits data to supersymmetry (SUSY) and supergravity (SUGRA) models illustrates, the targets of these beyond the Standard Model (BSM) SUSY and SUGRA models are anything but random. Some of the assumptions include the following:
* Dark matter has a particle nature and is composed primarily of the lightest stable supersymmetric particle (the LSP). Usually, this is accomplished with conservation of a supersymmetric quantum number called R-parity, although sometimes R-parity conservation is only approximate allowing for an unstable LSP with a lifetime on the order of the lifetime of the universe.
* Neutrinos are Majorana particles. Often a see-saw model and right handed neutrinos are assumed as well.
* None of the Standard Model particles are super-partners of each other.
* SUSY and SUGRA models are embedded in a larger grand unified theory (GUT) that gives rise to gauge coupling unification at a GUT scale.
* The extended boson sector of SUSY And SUGRA do not create any new fundamental forces with new fields that have additional coupling constants, and certainly not to any with phenomenological importance that is observed empirically.
* The gluons, the photon and the graviton are the only zero mass particles.
I'm sure that there are other important assumptions that I've overlooked.
Suppose that you remove the assumption that there is a stable or metastable LSP because dark matter phenomena can be fully understood as arising from graviton self-interactions (as proposed, for example, by Alexandre Deur) not properly accounted for in general relativity, rather than from dark matter particles. This would make R-parity conservation unnecessary (and indeed, maybe even preferable to do without to avoid creating additional kinds of dark matter which have not been detected experimentally). The lack of the need for an LSP also reduces pressure on the need for an LSP that is fairly close to the electroweak scale in mass.
Also, suppose that supersymmetric particles exist at high energy scales far in excess of the electroweak scale, for example, with masses on the order of 1-50+ TeV, as LHC results to date strongly suggest, although relaxing the assumption that there is a stable or metastable LSP also greatly opens up the parameter space of supersymmetry. This masses might be tied not to the ordinary Higgs boson (which would be the light scalar little h Higgs boson in this scenario), but to a heavy quartet of Higgs bosons (A, H, H+ and H-) at masses of the same order of magnitude as the mass scale of the heaviest supersymmetric particles.
Naively, this would lead us to expect that it is highly likely that supersymmetric particles would have very short lifetimes, presumably far shorter than those of the top quark, Higgs boson, W boson and Z boson which are currently the most short lived known particles (although how a particle could experience W boson weak decay in a time period of less than the W boson lifetime is problematic, perhaps a W' boson would be necessary).
Of course, while this would make fitting experimental data easier, it isn't obvious that this achieves much in terms of explanatory power. Certainly, for example, it does little to solve the hierarchy problem in a "natural" way which was a major motivator for SUSY in the first place.