This was one theoretical motivation for Grand Unified Theories themselves, and adding new interactions at any intermediate energy scale generally disrupts this gauge coupling unification.
The fact that the convergence in the Standard Model is actually inexact, however, is one of the key theoretical arguments against the Desert, since making the unification exact requires new physics below the GUT scale.
Above these energies, desert theory with the assumption of supersymmetry predicts no particles will be discovered until reaching the scale of approximately 1025 eV.
Presumably, even if the energy achieved in the LHC, ~ 1013 eV, were increased by up to 12 orders of magnitude, this would only result in producing more copious amounts of the particles known today, with no underlying structure being probed.
Indicative examples of the order of magnitude of the corresponding masses and fermion mixing parameters in accordance with experimental data have been calculated within the context of katoptrons.