Multiple infinite clusters conjecture for percolation with constant freezing

Let $d\geq 3$ and consider the percolation with constant freezing (PCF) process on $\mathbbm{Z}^d$, with edge-opening rate $1$ and freezing rate $\alpha>0$. Multiple infinite clusters conjecture. If $\alpha$ is sufficiently small, then the final distribution of the rate-$\alpha$ PCF process has positive probability of containing at least two infinite clusters. The heuristic is that, in dimensions at least three, an infinite cluster can form and freeze, leaving enough warm closed edges for a subsequent infinite cluster to form. The supplied source gives no resolution, so the conjecture remains open.