  Searches for supersymmetry (SUSY) often rely on a combination of hard physics
objects (jets, leptons) along with large missing transverse energy to separate
New Physics from Standard Model hard processes. We consider a class of
``double-invisible'' SUSY scenarios: where squarks, stops and sbottoms have a
three-body decay into two (rather than one) invisible final-state particles.
This occurs naturally when the LSP carries an additional conserved quantum
number under which other superpartners are not charged. In these topologies,
the available energy is diluted into invisible particles, reducing the observed
missing energy and visible energy. This can lead to sizable changes in the
sensitivity of existing searches, dramatically changing the qualitative
constraints on superpartners. In particular, for m_LSP>160 GeV, we find no
robust constraints from the LHC at any squark mass for any generation, while
for lighter LSPs we find significant reductions in constraints. If confirmed by
a full reanalysis from the collaborations, such scenarios allow for the
possibility of significantly more natural SUSY models. While not realized in
the MSSM, such phenomenology occurs naturally in models with mixed sneutrinos,
Dirac gauginos and NMSSM-like models.
