Multiplicative fractional list-coloring conjecture

Let $G$ be a graph with demand function $f$, and let $N$ be a common denominator for $f$. An $f$-fold $L$-coloring assigns to each vertex $v$ a subset of its list $L(v)$, with disjoint assigned sets on adjacent vertices and at least $Nf(v)$ colors assigned to $v$. The graph is $(f,N)$-list-colorable if this holds for every $N$-list-assignment $L$.

Multiplicative fractional list-coloring conjecture. If $G$ is $(f,N)$-list-colorable, then $G$ is $(f,mN)$-list-colorable for every positive integer $m$.

This is a fractional analogue of the multiplicative list-coloring problem. The source provides no resolution, so the conjecture remains open.