  Within the assumption of Left-Handed (LH) New Physics (NP), we review the
relations between $\mathcal{B}(B\to K^{(\ast)} \tau^+\tau^-)$ and
$\mathcal{B}(B\to K^{(\ast)} \nu\bar \nu)$ for several Beyond the Standard
Model (BSM) scenarios, commonly considered to explain the Lepton flavor
Universality (LFU) violation observed in charged and neutral-current
semileptonic $B$ decays. We employ the latest $R_{D^{(\ast)}}$ world averages
that include the recent LHCb measurement and assess the possibility of
simultaneously explaining the $B$-anomalies without spoiling current bounds on
di-neutrino and di-tau modes. This is particularly relevant in light of the
upcoming results by Belle II on neutrinos and the continuing improvement in
accuracy and sensitivity achieved in tau modes.
