This talk will focus on the tension between rigidity and multiple models for groupoid C*-algebras. If a C*-algebra $A$ admits a $\Gamma$-Cartan subalgebra $B$, then Brown, Fuller, Pitts, and Reznikoff showed that there is a unique groupoid $H$, satisfying certain hypotheses, and a twist $\Sigma$ over $H$ so that $A \cong C^*_r(H; \Sigma)$ and $B \cong C_0(H^{(0)})$. However, we show in joint work with Jonathan Brown that many twisted groupoid C*-algebras $C^*_r(G, \omega)$ admit $\Gamma$-Cartan subalgebras, even when $G$ does not satisfy the hypotheses of BFPR. Thus, we have two groupoid models for these C*-algebras: $C^*_r(G, \omega) \cong C^*_r(H; \Sigma)$. How are the two groupoids related? In this talk, we will describe the situations when $C^*_r(G, \omega)$ admits a $\Gamma$-Cartan subalgebra; explain how to construct $H$ from $G$ in these cases; discuss which groupoids $H$ can arise from this construction; and show how to reconstruct the groupoid $G$ from such an $H$.