Tensor indecomposability conjecture for existentially closed factors

Let $\mathcal E$ denote the class of existentially closed II$_1$ factors. Tensor indecomposability conjecture. For every $P\in\mathcal E$, there do not exist II$_1$ factors $A$ and $B$, with $B$ full, such that

$$P\cong A\overline\otimes B.$$

The conjecture extends the paper's theorem for the class $\mathcal {ET}$ to all existentially closed factors and would rule out tensor decompositions with a full factor.