The collapse of phase-separating single, supported lipid bilayers, consisting of mixtures of a zwitterionic phospholipid (POPC) and an anionic lipid (DPPA) upon thermal annealing in the presence of ions is examined using a combination of scanning probe, epifluorescence, and ellipsometric microscopies. We find that thermal annealing in the presence of ions in the bathing medium induces an irreversible transition from domain-textured, single supported bilayers to one comprising islands of multibilayer stacks, whose lateral area decays with lamellarity, producing pyramidal staircase "mesa" topography. The higher order lamellae are almost invariably localized above the anionic-lipid rich, gel-phase domains in the parent bilayer and depends on the ions in the bathing medium. The collapse mechanism appears to involve synergistic influences of two independent mechanisms: (1) stabilization of the incipient headgroup-headgroup interface in the emergent multibilayer configuration facilitated by ions in the bath and (2) domain-boundary templated folding. This collapse mechanism is consistent with previous theoretical predictions of topography-induced rippling instability in collapsing lipid monolayers and suggests the role of the mismatch in height and/or spontaneous curvature at domain boundaries in the collapse of phase-separated single supported bilayers.