The infinite virtual connect-sum conjecture

Let $V_1$ and $V_2$ be non-classical, weakly prime virtual links. A connect sum of $V_1$ and $V_2$ is a virtual link obtained by joining them along arcs in their diagrams.

Infinite virtual connect-sum conjecture. There are infinitely many distinct virtual links that decompose as a connect sum of $V_1$ and $V_2$.

This generalizes the preceding result for non-classical, weakly prime, alternating virtual links, for which the stated construction produces infinitely many distinct connect sums. The conjecture concerns whether the same phenomenon holds without the alternating hypothesis.