For a symmetric monoidal category $\mathbf{C}$, and a given collection of objects $\mathbf{W}$, we provide a construction of $\mathbf{C}\mathbf{\{W\}}$, which results from $\mathbf{C}$ by adding monoidal indeterminates $x{\{O\}}:{I}\to{O}$ for every object $O$ of $\mathbf{W}$. As a special case, we solve the problem of explicitly adding an indeterminate to a single object $O$ in $\mathbf{C}$. Furthermore, if $\mathbf{C}$ is closed, so is $\mathbf{C}\mathbf{\{W\}}$. By suitably restricting the morphisms in $\mathbf{C}\mathbf{\{W\}}$, we obtain the categories of possible worlds of Oles and Tennent, thereby providing a universal characterisation for these constructions.