The global asymptotic matching equations for multiple coupled resistive modes of arbitrary parity in a cylindrical plasma are derived. Three different variational principles are given for the outer region matching data, while the inner region analysis features a careful treatment of the symmetry‐breaking effect of a gradient in the equilibrium current for a zero‐&bgr; slab model. It is concluded that the usual constant‐&psgr; result remains valid and constrains the matrix matching formalism. The dispersion relation is compared with initial value calculations of a double tearing mode when there are small relative rotation velocities between the rational surfaces. In treating differential rotation within the asymptotic matching formalism, flow is ignored in the outer region and is assumed to affect the inner response solely through a Doppler shift. It is shown that the relative rotation can have a strong stabilizing effect by making all but one rational surface effectively ideal.