The sources of the astrophysical neutrino flux discovered by IceCube are for the most part unresolved. Extragalactic core-collapse supernovae (CCSNe) have been suggested as candidate multi-messenger sources. In interaction-powered supernovae, a shock propagates in a dense circumstellar medium (CSM), producing a bright optical emission and potentially accelerating particles to relativistic energies. Shock interaction is believed to be the main energy source for Type IIn supernovae (identified by narrow lines in the spectrum), hydrogen-rich superluminous supernovae and a subset of hydrogen-poor superluminous supernovae. Production of high-energy neutrinos is expected in collisions between the accelerated protons in the shocks and the cold CSM particles. We select a catalog of interaction-powered supernovae from the Bright Transient Survey of the Zwicky Transient Facility. We exploit a novel modeling effort that connects the time evolution of the optical emission to the properties of the ejecta and the CSM, allowing us to set predictions of the neutrino flux for each source. In this contribution, we describe a stacking search for high-energy neutrinos from this population of CCSNe with the IceCube Neutrino Observatory.