  We explore the phenomenology of having a second epoch of dark matter
annihilation into dark radiation long after the standard thermal freeze-out.
Such a hidden reannihilation process could affect visible sectors only
gravitationally. As a concrete realization we consider self-interacting dark
matter (SIDM) with a light force mediator coupled to dark radiation. We
demonstrate how resonantly Sommerfeld enhanced cross sections emerge to induce
the reannihilation epoch. The effect is a temporally local modification of the
Hubble expansion rate and we show that the Cosmic Microwave Background (CMB)
measurements -- as well as other observations -- have a high sensitivity to
observe this phenomenon. Special attention is given to the model region where
late kinetic decoupling and strong self-interactions can alleviate several
small-scale problems in the cold dark matter paradigm at the same time.
Interestingly, we find that reannihilation might here also simultaneously lower
the tension between CMB and low-redshift astronomical observations of $H_{0}$
and $\sigma_{8}$. Moreover, we identify reannihilation as a clear signature to
discriminate between the phenomenologically otherwise almost identical vector
and scalar mediator realizations of SIDM.
