Let \$M\$ be a representable matroid and \$Q, R, S, T\$ subsets of the ground set such that the smallest separation that separates \$Q\$ from \$R\$ has order \$k\$, and the smallest separation that separates \$S\$ from \$T\$ has order \$l\$. We prove that if \$M\$ is sufficiently large, then there is an element \$e\$ such that in one of \$M\backslash e\$ and \$M\!/e\$ both connectivities are preserved. 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.