  In this paper we study duoidal structures on $\infty$-categories of operadic
modules. Let $\mathcal{O}^{\otimes}$ be a small coherent $\infty$-operad and
let $\mathcal{P}^{\otimes}$ be an $\infty$-operad. If a
$\mathcal{P}\otimes\mathcal{O}$-monoidal $\infty$-category
$\mathcal{C}^{\otimes}$ has a sufficient supply of colimits, then we show that
the $\infty$-category ${\rm Mod}_A^{\mathcal{O}}(\mathcal{C})$ of
$\mathcal{O}$-$A$-modules in $\mathcal{C}^{\otimes}$ has a structure of
$(\mathcal{P},\mathcal{O})$-duoidal $\infty$-category for any
$\mathcal{P}\otimes\mathcal{O}$-algebra object $A$.
