In Sharpe's book on Cartan geometry, he mentions in kind of an offhand way that Cartan atlases extend to unique maximal Cartan atlases, but I'm feeling skeptical. For a Klein pair $(G,H)$ with Lie algebras $(\mathfrak{g},\mathfrak{h})$, a Cartan atlas is defined as a family of $\mathfrak{g}$-valued $1$ forms on an open cover such that on the overlap of any two open charts $U$ and $V$ there exists a smooth function $k:U\cap V\to H$ with $$\theta_U=\mathrm{Ad}(k^{-1})\theta_V+k^* \omega_H,\tag{1}\label{eq1}$$ where $\omega_H$ is the Maurer-Cartan form on $H$.
The standard way to prove that an atlas extends to a unique maximal atlas is to union all atlases compatible with a given one and prove that all such atlases are compatible with each other. So if $\mathcal{A}\sim \mathcal{B}$ and $\mathcal{B}\sim \mathcal{C}$ then we should get $\mathcal{A}\sim \mathcal{C}.$ Given $U\in \mathcal{A}$ and $V\in \mathcal{C}$ with nonempty intersection, we cover $U\cap V$ with charts from $\mathcal{B}$. On each of these neighborhoods $W_i\cap U\cap V$ with $W_i\in \mathcal{B}$ we get compatibility of $\theta_U$ with $\theta_V$. The hitch is that the functions $k_i:U\cap V\cap W_i\to H$ may not patch together to a single function $k:U\cap V\to H$ providing a transition between $\theta_U$ and $\theta_V$.
Any two transition maps satisfying equation \eqref{eq1} will differ by left multiplication by a smooth function into the kernel $K$ of $(G,H)$ (the largest normal subgroup of $G$ contained in $H$). In the case where the geometry $(G,H)$ is effective and $K=\{e\}$, transition maps are unique, so each of the $k_i$ will definitely patch together. In general, for Klein pairs $(G,H)$ that are only locally effective with discrete $K$, it is not totally clear that a similar argument will succeed. So does there exist a unique maximal atlas in this case?
This answer is speculative, so I welcome someone else to post a better one. I believe that transitivity of compatibility of atlases fails in general. The problem is essentially that two charts can be compatible locally without being compatible globally (I think) when their intersection is not simply connected.
This seems like a pathological state of affairs, and so in the ineffective case of Cartan geometry, it would seem more natural to force localness of compatibility and say that two charts are compatible if there exists a $k$ inducing the appropriate change of gauge in a neighborhood of each point of the intersection. With this altered definition we would recover the existence of unique maximal atlases by the argument I sketched in my question.