  Nonstandard on-shell decays of $W^\pm$ and $Z$ bosons are possible within the
framework of extended supersymmetric models, i.e., with singlet states and/or
new couplings compared to the minimal supersymmetric standard model. These
modes are typically encountered in regions of the parameter space with light
singlet-like scalars, pseudoscalars, and neutralinos. In this letter we
emphasize how these states can lead to novel signals at colliders from $Z$- or
$W^\pm$-boson decays with prompt or displaced multileptons/tau
jets/jets/photons in the final states. These new modes would give distinct
evidence of new physics even when direct searches remain unsuccessful. We
discuss the possibilities of probing these new signals using the existing LHC
run-I data set. We also address the same in the context of the LHC run-II, as
well as for the future colliders. We exemplify our observations with the "$\mu$
from $\nu$" supersymmetric standard model, where three generations of
right-handed neutrino superfields are used to solve shortcomings of the minimal
supersymmetric standard model. We also extend our discussion for other variants
of supersymmetric models that can accommodate similar signatures.
