Let $C$ be a $k$-linear ($Vect_k$-enriched) monoidal category and consider the 2-category $Mod_{C}$ of $k$-linear $(C,C)$-bimodule categories in the sense of Ostrik (https://arxiv.org/abs/math/0111139.). Roughly speaking, this construction can be thought of as a ``categorification" of a module over a ring. Let $\otimes_C$ denote the tensor product of $k$-linear $(C,C)$-bimodule categories(as defined in the work of Douglas, Schommer-Pries, and N. Snyder in https://arxiv.org/abs/1406.4204.)
Does $\otimes_C$ endow $Mod_{C}$ with the structure of a monoidal 2-category?