Too many X's, Y's and Z's?

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.