  Studies of R-parity violating (RPV) supersymmetry typically assume that
nucleon stability is protected by approximate baryon number (B) or lepton
number (L) conservation. We present a new class of RPV models that violate B
and L simultaneously (BLRPV), without inducing rapid nucleon decay. These
models feature an approximate $Z_2^e \times Z_2^\mu \times Z_2^\tau$ flavor
symmetry, which forbids 2-body nucleon decay and ensures that flavor
antisymmetric $L L E^c$ couplings are the only non-negligible L-violating
operators. Nucleons are predicted to decay through $N \rightarrow K e \mu \nu$
and $n \rightarrow e \mu \nu$; the resulting bounds on RPV couplings are rather
mild. Novel collider phenomenology arises because the superpartners can decay
through both L-violating and B-violating couplings. This can lead to, for
example, final states with high jet multiplicity and multiple leptons of
different flavor, or a spectrum in which depending on the superpartner, either
B or L violating decays dominate. BLRPV can also provide a natural setting for
displaced $\tilde{\nu} \rightarrow \mu e$ decays, which evade many existing
collider searches for RPV supersymmetry.
