I saw a theorem saying that any atlas on a manifold can be extended to a unique maximal atlas.
Concerning the standard atlas of $\mathbb{R}^n$, we saw that this was the atlas generated by the chart $(\mathbb{R^n}, Id_{\mathbb{R}^n})$. So what does it contain? My guess is that it contains every diffeomorphism (here by diffeomorphism I mean the usual notion of diffeomorphism of $\mathbb{R^n}$) (but on what sets???). Indeed contains $(\mathbb{R^n}, Id_{\mathbb{R}^n})$ and it is smoothly compatible since a composition of diffeomorpism is a diffeomorphism.
The standard atlas of $\mathbb{R}^n$ just contains one chart: the set $\mathbb{R}^n$ with the map $Id_{\mathbb{R}^n}$, which is a diffeomorphism. Since you have only one chart you don't have to care about transition maps.