  We study SUSY signatures at the 7, 8 and 14 TeV LHC employing the
19-parameter, R-Parity conserving p(henomenological)MSSM, in the scenario with
a neutralino LSP. Our results were obtained via a fast Monte Carlo simulation
of the ATLAS SUSY analysis suite. The flexibility of this framework allows us
to study a wide variety of SUSY phenomena simultaneously and to probe for weak
spots in existing SUSY search analyses. We determine the ranges of the
sparticle masses that are either disfavored or allowed after the searches with
the 7 and 8 TeV data sets are combined. We find that natural SUSY models with
light squarks and gluinos remain viable. We extrapolate to 14 TeV with both 300
fb$^{-1}$ and 3 ab$^{-1}$ of integrated luminosity and determine the expected
sensitivity of the jets + MET and stop searches to the pMSSM parameter space.
We find that the high-luminosity LHC will be powerful in probing SUSY with
neutralino LSPs and can provide a more definitive statement on the existence of
natural Supersymmetry.
