  In this note we consider boundary perturbations in the A-Series unitary
minimal models by phi_{r,r+2} fields on superpositions of boundaries. In
particular, we consider perturbations by boundary condition changing operators.
Within conformal perturbation theory we explicitly map out the space of
perturbative renormalisation group flows for the example phi_{1,3} and find
that this sheds light on more general phi_{r,r+2} perturbations. Finally, we
find a simple diagrammatic representation for the space of flows from a single
Cardy boundary condition.
