  We prove a Desch-Schappacher type perturbation theorem for one-parameter
semigroups on Banach spaces which are not strongly continuous for the norm, but
possess a weaker continuity property. In this paper we chose to work in the
framework of bi-continuous semigroups. This choice has the advantage that we
can treat in a unified manner two important classes of semigroups: implemented
semigroups on the Banach algebra $\mathscr{L}(E)$ of bounded, linear operators
on a Banach space $E$, and semigroups on the space of bounded and continuous
functions over a Polish space induced by jointly continuous semiflows. For both
of these classes we present an application of our abstract perturbation theorem
