  Observations of some supernovae (SNe), such as SN 2014C, in the X-ray and
radio wavebands revealed a rebrightening over a timescale of about a year since
their detection. Such a discovery hints towards the evolution of a
hydrogen-poor SN of Type Ib/c into a hydrogen-rich SN of Type IIn, the late
time activity being attributed to the interaction of the SN ejecta with a dense
hydrogen-rich circumstellar medium (CSM) far away from the stellar core. We
compute the neutrino and gamma-ray emission from these SNe, considering
interactions between the shock accelerated protons and the non-relativistic CSM
protons. Assuming three CSM models inspired by recent electromagnetic
observations, we explore the dependence of the expected multi-messenger signals
on the CSM characteristics. The detection prospects of existing and upcoming
gamma-ray (Fermi-LAT and Cerenkov Telescope Array) and neutrino (IceCube and
IceCube-Gen2) telescopes are also outlines. Our findings are in agreement with
the non-detection of neutrinos and gamma-rays from past SNe exhibiting late
time emission. Nevertheless, the detection prospects of SNe with late time
emission in gamma-rays and neutrinos with the Cerenkov Telescope Array and
IceCube-Gen2 (Fermi-LAT and IceCube) are promising and could potentially
provide new insight into the CSM properties, if the SN burst should occur
within $10$ Mpc ($4$ Mpc).
