A spherical variety is a normal variety $X$ together with an action of a connected reductive affine algebraic group $G$, a Borel subgroup $B\subset G$, and a base point $x_0\in X$ such that the $B$-orbit of $x_0$ in $X$ is a dense open subset of $X$.

A wonderful variety is a smooth complete variety $X$ with the action of a semisimple simply connected group $G$ such that there is a point $x_0\in X$ with open $G$ orbit and such that the complement $X\setminus G\cdot x_0$ is a union of prime divisors $E_1,\cdots, E_t$ having simple normal crossing, and such that the closures of the $G$-orbits in $X$ are the intersections $\bigcap_{i\in I}E_i$ where $I$ is a subset of $\{1,\dots, t\}$.

Now, fix a connected reductive affine algebraic group $G$ and a Borel subgroup $B\subset G$. Could there exist two non isomorphic smooth complete varieties that are spherical with respect to $(G,B)$ and wonderful with respect to $G$ ?