  Let $M$ be a representable matroid, and $Q, R, S, T$ subsets of the ground
set. We prove that, if $M$ is sufficiently large, then there is an element $e$
such that deleting or contracting $e$ preserves both the $Q$-$R$ and the
$S$-$T$ connectivities. For matroids representable over a finite field we prove
a stronger result: we show that we can remove $e$ such that both a connectivity
and a minor of $M$ are preserved.
