We consider first order perturbations on locally rotationally symmetric (LRS) class II spacetimes. In particular, we investigate the interactions between electromagnetic, gravitational, and plasma related perturbations when allowing for a non-zero magnetic field on the background spacetime. In doing so we focus on mechanisms for generating and magnifying the magnetic fields, as these kinds of mechanisms may have some relevance when trying to explain the origin of the observed large scale cosmic magnetic fields. The equations governing the behavior of the perturbations are gathered from the Ricci identities for certain preferred vector fields, the Bianchi identities, Maxwell's equations, and from relations describing energy-momentum conservation and particle conservation for the cosmological plasma. After employing a simplified cold magnetohydrodynamic (MHD) description, and harmonically decomposing the spatial dependencies, we arrive at a closed set of ordinary differential equations in time. On analyzing this system, which decouples into an even and an odd subsector, we indeed observe possible mechanisms for generating magnetic field perturbations to first order.