Conformational phase transitions of macromolecules are an important class of problems in fundamental polymer physics. While the conformational phase transitions of linear DNA have been extensively studied, this feature of topologically complex DNA remains unexplored. We report herein the polymer-and-salt-induced (Ψ) phase transition of 2D catenated DNA networks, called kinetoplasts, using single-molecule fluorescence microscopy. We observe that kinetoplasts can undergo a reversible transition from the flat phase to the collapsed phase in the presence of NaCl as a function of the crowding agent poly(ethylene glycol). The nature of this phase transition is tunable through varying ionic strengths. For linear DNA, the coexistence of coil and globule phases was attributed to a first order phase transition associated with a double well potential in the transition regime. Kinetoplasts, however, navigate from the flat to the collapsed phase by passing through an intermediate regime, characterized by the coexistence of a multipopulation with varying shapes and sizes. Conformations of individual molecules in the multipopulation are long-lived, which suggests a rugged energy landscape.