  We examine transmission through a quantum graph vertex to which auxiliary
edges with constant potentials are attached. We find a characterization of
vertex couplings for which the transmission probability from a given "input"
line to a given "output" line shows a flat passband. The bandwidth is
controlled directly by the potential on the auxiliary edges. Vertices with such
couplings can thus serve as controllable band-pass filters. The paper extends
earlier works on the topic. The result also demonstrates the effectivity of the
$ST$-form of boundary conditions for a study of scattering in quantum graph
vertices.
