  Heavy meson spectroscopy above open flavor thresholds has become a challenge
both from the experimental and theoretical points of view. Experimentally,
several signals have been interpreted as meson resonances with unusual
properties; theoretically, such signals may be identified with meson-meson
molecules or compact multiquark structures. We analyze the influence of
thresholds on heavy meson spectroscopy comparing different flavor sectors and
quantum numbers. The validity of a quark-model picture above open-flavor
thresholds would severely restrict the number of channels that may lodge
multiquark structures as meson-meson molecules.
