  With substantial evidence of glassy behavior in the phase diagram of high
$T_c$ superconductors and its co-existence with superconductivity, we attempt
to answer the question: what are the properties of a superconducting state
where the force driving cooper pairing becomes dissipative? We find that when
the bosonic mediator is local, dissipation acts to reduce the superconducting
critical temperature ($T_c$). On the other hand, contrary to na\"{i}ve
expectations, $T_c$ behaves non-monotonically with dissipation for a non-local
mediator -- weakly dissipative bosons at different energy scales act coherently
to give rise to an increase in $T_c$ and eventually destroy superconductivity
when the dissipation exceeds a critical value. The critical value occurs when
dissipative effects become comparable to the energy scale associated with the
spatial stiffness of the mediator, at which point, $T_c$ acquires a maximum. We
outline consequences of our results to recent proton irradiation experiments
(M. Leroux et al.,~\cite{Welp2018}) on the cuprate superconductor
La$_{2-x}$Ba$_x$CuO$_4$ (LBCO) which observe a disorder induced increase in
$T_c$ even when the transition temperature of the proximate charge density wave
(CDW) is unaffected by the presence of irradiation. Our mechanism is a novel
way to raise $T_c$ that does not require a `tug-of-war' -type scenario between
two competing phases.
