  A fibered concordance of knots, introduced by Harer, is a concordance between
fibered knots that is well-behaved with respect to the fibrations. We consider
semi-fibered concordance of two component ordered links $L=J \sqcup K$ with $J$
fibered. These are concordances that restrict to fibered concordances on the
first component. Motivated by some examples of Gompf-Scharlemann-Thompson, we
further limit our attention to those links $L$ where $K$ is "close to" a fiber
of $J$. Such $L$ are studied with virtual covers, where a virtual knot
$\upsilon$ is associated to $L$. We show that the concordance class of
$\upsilon$ is a semi-fibered concordance invariant. This gives obstructions for
certain slice and ribbon discs for the $K$ component. Further applications are
to injectivity of satellite operators in semi-fibered concordance and to knots
in fibered $3$-manifolds.
