Semistability conjecture for relatively hyperbolic groups

Let $G$ be a finitely generated group hyperbolic relative to a finite collection $\{P_1,\ldots,P_n\}$ of proper finitely generated subgroups. Semistability conjecture. If each $P_i$ has semistable fundamental group at $\infty$, then $G$ has semistable fundamental group at $\infty$. This conjecture asks whether semistability at infinity passes from peripheral subgroups to a relatively hyperbolic group; it is the primary semistability question left open after the known result for relatively hyperbolic groups whose boundary has no cut point.