The two-Kuratowski-edge conjecture for simultaneous crossing-criticality

Let $G$ be a graph, and let $e$ and $f$ be Kuratowski edges of $G$, meaning that each belongs to a subgraph homeomorphic to $K_{3,3}$ or $K_5$. A graph obtained by multiplying edges of $G$ is formed by adding parallel edges to edges of $G$. Two-Kuratowski-edge conjecture. There exists a graph $H$, obtained by multiplying edges of $G$, such that both $e$ and $f$ are crossing-critical in $H$.

This is presented as the immediate next step toward the Kuratowski-edge conjecture. The paper proves that a single Kuratowski edge can be made crossing-critical, while simultaneous crossing-criticality for two such edges is stated as difficult and remains open.