In this chapter, we discuss another class of perturbations, the so-called Desch–Schappacher perturbations. They provide a powerful framework for extending the perturbation theory of bi-continuous semigroups beyond the bounded and Miyadera–Voigt classes, discussed in Chapter 7 . Desch–Schappacher perturbations demand a deeper understanding of the interplay between the generator and extrapolation spaces that were discussed in Chapter 4 and Chapter 5 . These spaces, constructed to accommodate unbounded perturbations, allow for the definition of perturbed operators that might not be well-defined on the original space. By employing this framework, one ensures the perturbed operator still generates a bi-continuous semigroup, maintaining the structural stability of the dynamics. In this chapter, we formulate and prove a Desch–Schappacher-type perturbation theorem for bi-continuous semigroups, showing that for a certain class of admissible operators the perturbation of a generator of a bi-continuous semigroup still gives rise to a semigroup generator.