The basepoint free conjecture for smooth projective threefolds in positive characteristic

Let $k$ be an algebraically closed field of positive characteristic. Let $X$ be a smooth projective threefold over $k$, let $S$ be a smooth prime divisor on $X$, and let $A$ be an ample Cartier divisor on $X$ such that $K_X+S+A$ is nef.

Basepoint free conjecture. The linear system $|b(K_X+S+A)|$ is basepoint free for every $b\gg 0$.

This conjecture is presented as a comparison with the threefold extension theorem and the trace-map result, in the case where the relevant surface has Kodaira dimension zero. Its resolution status is not specified in the supplied text.