Peterson's unique maximal amenable extension conjecture for free group factors

Let $L(\mathbb{F}_n)$ be a free group factor and let $B\subset L(\mathbb{F}_n)$ be a diffuse amenable subalgebra. A maximal amenable extension of $B$ is an amenable subalgebra of $L(\mathbb{F}_n)$ containing $B$ that is maximal with respect to inclusion. Peterson's conjecture. Every diffuse amenable subalgebra of a free group factor $L(\mathbb{F}_n)$ has a unique maximal amenable extension inside $L(\mathbb{F}_n)$. This conjecture proposes a stronger structural property than strong solidity for free group factors, asserting uniqueness of the maximal amenable enlargement of every diffuse amenable subalgebra; its status is not resolved in the supplied context.