`Wedgebox' plots constructed by plotting the di-electron invariant mass versus the di-muon invariant mass from pp -> e^+e^- mu^+ mu^- + missing energy signature LHC events. Data sets of such events are obtained across the MSSM input parameter space in event-generator simulations, including cuts designed to remove SM backgrounds. Their study reveals several general features: (1)Regions in the MSSM input parameter space where a sufficient number of events are expected so as to be able to construct a clear wedgebox plot are delineated. (2)The presence of box shapes on a wedgebox plot either indicates the presence of heavy Higgs bosons decays or restricts the location to a quite small region of low μ and M_2 values \lsim 200 GeV, a region denoted as the `lower island'. In this region, wedgebox plots can be quite complicated and change in pattern rather quickly as one moves around in the (μ, M_2) plane. (3)Direct neutralino pair production from an intermediate Z^{0*} may only produce a wedge-shape since only \widetilde{\chi}_2^0\widetilde{\chi}_3^0 decays can contribute significantly. (4)A double-wedge or wedge-protruding-from-a-box pattern on a wedgebox plot, which results from combining a variety of MSSM production processes, yields three distinct observed endpoints, almost always attributable to \widetilde{\chi}_{2,3,4}^0 \to \widetilde{\chi}_1^0 \ell^+\ell^- decays, which can be utilized to determine a great deal of information about the neutralino and slepton mass spectra and related MSSM input parameters. Wedge and double-wedge patterns are seen in wedgebox plots in another region of higher μ and M_2 values, denoted as the`upper island.' Here the pattern is simpler and more stable as one moves across the (μ, M_2) input parameter space. ; Comment: 28 pages (LaTeX), 8 figures (encapsulated postscript)