Let $\displaystyle M$ be a topological manifold, and let $\displaystyle \mathcal{A}$ be a smooth atlas. Then I understand that $\displaystyle \mathcal{A}$ is contained in a unique maximal smooth atlas, $\displaystyle \overline{\mathcal{A}}$, the collection of charts which are smoothly compatible with the charts in $\displaystyle \mathcal{A}.$

Now let $\displaystyle M$ be a topological manifold with boundary, and let $\displaystyle \mathcal{A}$ be a smooth atlas. My question is, is $\displaystyle \mathcal{A}$ contained in a unique maximal smooth atlas in a similar way to the manifold without boundary case?

Thanks for any advice.