Let $G$ be a group acting by isometries on a hyperbolic space $X$. Given geometrically natural subgroups $H$ and $K$ of $G$, it is natural to ask whether $ \langle H, K \rangle $ inherits the geometric properties of $H$ and $K$, and whether $ \langle H, K \rangle $ admits a nice algebraic structure. In a classical work of Gitik we receive an answer in the case where $G$ is a hyperbolic group, and $H$ and $K$ are quasiconvex. In more recent work of Martínez-Pedroza and Sisto, we receive an answer in the case where $G$ is relatively hyperbolic, and $H$ and $K$ are relatively quasiconvex. In this talk, I will discuss a generalization of a combination theorem of Abbot and Manning that covers a broader class of geometrically natural subgroups of such a group $G$. This is still a work in progress.