It is now well known that details in the intermolecular potential can significantly affect the qualitative features of a phase diagram where temperature is plotted against density for the coexistence curves among fluid and solid phases. While previous calculations of phase diagrams have assumed a time-invariant potential function, this report concerns the phase diagram for "breathing" molecules, i.e. molecules whose strength of intermolecular attraction fluctuates in time. Such fluctuations can occur in biomacromolecules where an active site can switch between"on" and "off' positions. Phase-equilibrium calculations were performed for molecules that have a periodic (breathing) attractive force in addition to the conventional intermolecular forces. The phase diagram for such molecules is as expected when the "breathing" properties are independent of density. However, when (more realistically), the "breathing" properties are density-dependent, the phase diagram exhibits dramatic changes. These calculations may be useful for interpreting experimental data for protein precipitation, for plaque formation in blood vessels and for scaffold-supported tissue formation.