  Processes of the form $pp\to anything \to X_i X_j \to x\bar{x} + y\bar{y} (+
\slashchar{E})$ are studied via a technique that may be viewed as an adaptation
of time-honoured Dalitz plot analyses. $X_i$ and $X_j$ are new heavy states
(with $i,j=1...n$), which may be identical or distinct; and $x\bar{x}$ and
$y\bar{y}$ are necessarily distinct Standard Model (SM) fermion pairs whose
invariant masses can be measured. A Dalitz-like plot of said invariant masses,
$M(x\bar{x})$ {\it vs.$$} $M(y\bar{y})$, exhibits a topology connected to the
masses and specific decay chains of $X_i$ and $X_j$. Aside from relatively
minor details, observed patterns consist of a collection of box and wedge
shapes. This collection is model-dependent: comparison of the observed pattern
to the possibilities for a specific model yields information on which new
particle pair combinations are actually being produced, information beyond that
extractable from conventional one-dimensional invariant mass distributions. The
technique is illustrated via application to the Minimal Supersymmetric Standard
Model (MSSM) process $pp \to
\tilde{g}\tilde{g},\tilde{g}\tilde{q},\tilde{q}\tilde{q} \to
\widetilde{\chi}_i^0 \widetilde{\chi}_j^0 \to e^+ e^- + \mu^+ \mu^- (+
\slashchar{E})$. Here the heavy states are neutralinos $\widetilde{\chi}_i^0$
($i=2,3,4$) -- note $\widetilde{\chi}_1^0$ is excluded -- which are produced in
gluino/squark ($\tilde{g}$/$\tilde{q}$) cascade decay chains. Even with fairly
modest expectations for the LHC performance during the first few years, this
method still provides substantial insight into the neutralino mass spectrum and
couplings if gluino/squark masses are relatively low ($\simeq 400 \hbox{GeV}$).
