We know quite certainly that the standard model is incomplete both from quantum theory and cosmology: If one rejects fine tuning, something has to keep the Higgs mass from diverging due to Top loops. Above a few TeV, something has to keep vector boson scattering cross sections sane. Dark matter and dark energy have to be made of something.
Unfortunately, that it is incomplete is about all the hell we've got at this point. The LHC has basically been ruling proposed SUSY models out unceasingly, and if we're unlucky and New Physics lies past 14TeV, it will likely be a damn long time until we discover it because the LHC took up the theoretical physics budgets of nearly every nation that does theoretical physics for the better part of a decade to build, and they already had the tunnel. To make significant advances with a successor hadron accelerator we'd be talking about building something at least several times larger and the obstacles are enormous... Staggering costs, the irradiation of the inner detectors, data processing, construction times stretching into multiple decades. Not to mention that the LHC consumed most of the world's supply of helium for years on end.
In the worst-case scenario, there's nothing significantly new until one reaches strong-force unification, and that lies a trillion times beyond the LHC,