  Simplified Models are a useful way to characterize new physics scenarios for
the LHC. Particle decays are often represented using non-renormalizable
operators that involve the minimal number of fields required by symmetries.
Generalizing to a wider class of decay operators allows one to model a variety
of final states. This approach, which we dub the $n$-body extension of
Simplified Models, provides a unifying treatment of the signal phase space
resulting from a variety of signals. In this paper, we present the first
application of this framework in the context of multijet plus missing energy
searches. The main result of this work is a global performance study with the
goal of identifying which set of observables yields the best discriminating
power against the largest Standard Model backgrounds for a wide range of signal
jet multiplicities. Our analysis compares combinations of one, two and three
variables, placing emphasis on the enhanced sensitivity gain resulting from
non-trivial correlations. Utilizing boosted decision trees, we compare and
classify the performance of missing energy, energy scale and energy structure
observables. We demonstrate that including an observable from each of these
three classes is required to achieve optimal performance. This work
additionally serves to establish the utility of $n$-body extended Simplified
Models as a diagnostic for unpacking the relative merits of different search
strategies, thereby motivating their application to new physics signatures
beyond jets and missing energy.
