The discovery of a Higgs boson with a mass of 126 GeV at the LHC when combined with the non-observation of new physics both in direct and indirect searches imposes strong constraints on supersymmetric models and in particular on the top squark sector. The experiments for direct detection of dark matter have provided with yet more constraints on the neutralino LSP mass and its interactions. After imposing limits from the Higgs, flavour and dark matter sectors, we examine the feasibility for a light stop in the context of the pMSSM, in light of current results for stop and other SUSY searches at the LHC. We only require that the neutralino dark matter explains a fraction of the cosmologically measured dark matter abundance. We find that a stop below $\sim$ 500 GeV is still allowed and we study various probes that could be performed at the LHC Run - II either through direct searches for the light and heavy stop, or SUSY searches not currently available in simplified model results. Moreover we study the characteristics of heavy Higgs and illustrate the parameter space with large cross sections to fermionic or electroweakino channels. Finally we show that nearly all scenarios with a small stop - LSP mass difference will be tested by Xenon1T provided the NLSP is a chargino, thus probing a region hard to access at the LHC.