  If the hints for light sterile neutrinos from short-baseline anomalies are to
be taken seriously, global fits indicate active-sterile mixings of a magnitude
comparable to the known reactor mixing. We therefore study the conditions under
which the active-sterile and reactor mixings could have the same origin in an
underlying flavour model. As a starting point, we use $\mu-\tau$ symmetry in
the active neutrino sector, which (for three neutrinos) yields a zero reactor
neutrino angle and a maximal atmospheric one. We demonstrate that adding one
sterile neutrino can change this setting, so that the active-sterile mixing and
non-zero $\theta_{13}$ can be generated simultaneously. From the
phenomenological perspective, electron (anti)neutrino disappearance can be
easily accommodated, while muon neutrino disappearance can vanish. It is,
however, difficult to reconcile the LSND results with this scenario. From the
theory perspective, the setting requires the misalignment of some of the flavon
vacuum expectation values, which may be achieved in an $A_4$ or $D_4$ flavour
symmetry model using extra dimensions.
