  We discuss the modes $B\to K^{(*)}\nu\bar\nu$ in the context of non-standard
neutrino interactions that add incoherently to the SM rates. We consider two
scenarios: an additional light neutrino; and neutrino lepton flavour violation.
We find that an additional light neutrino that interacts with SM fields via a
non-universal $Z^\prime$ can increase $R^\nu_{K^{(*)}}$ by up to a factor of
two without conflicting with $B_s-\bar B_s$ mixing. This model then predicts
rates for $B_s\to \tau^+\tau^-$ up to six times larger than the SM. In the
context of neutrino lepton flavour violation mediated by leptoquarks we find
that the current experimental upper bounds on $R^\nu_{K^{(*)}}$ are already
more constraining than direct bounds from $B_s\to \tau \ell$ and $B\to
K^{(*)}\tau \ell$ modes for $\ell=e,\mu$.
