  Spectroscopic measurements in quantum systems are subject to selection rules,
usually based on space-time symmetries, that allow or disallow transitions
between states. In many-body systems, in addition to the single-particle
states, there emerge new ones due to collective excitations of the system. Here
we demonstrate the existence of a "fragile" selection rule that emerges as a
manifestation of many-body effects and outlines the conditions for collective
excitations to couple to a given spectroscopic probe beyond the usual symmetry
considerations. As an example, we apply the rule to Raman spectroscopy of
multiband superconductors and settle some unresolved features in experiments.
