  We report the status of an ongoing lattice-QCD calculation of form factors
for exclusive semileptonic decays of $B$ mesons with both charged currents
($B\to\pi\ell\nu$, $B_s\to K\ell\nu$) and neutral currents
($B\to\pi\ell^+\ell^-$, $B\to K\ell^+\ell^-$). The results are important for
constraining or revealing physics beyond the Standard Model. This work uses
MILC's (2+1+1)-flavor ensembles with the HISQ action for the sea and light
valence quarks and the clover action in the Fermilab interpretation for the $b$
quark. Simulations are carried out at three lattice spacings down to $0.088$
fm, with both physical and unphysical sea-quark masses. We present preliminary
results for correlation-function fits.
