Cartan-free conjecture for existentially closed factors

Let $\mathcal E$ denote the class of existentially closed II$_1$ factors. A Cartan subalgebra is a maximal abelian subalgebra whose normalizer generates the factor. Cartan-free conjecture. There is no factor $P\in\mathcal E$ which has a Cartan subalgebra. The conjecture would strengthen the known obstruction to existentially closed factors arising as group-measure-space von Neumann algebras from non-inner amenable groups; its resolution is open.