Abstract We introduce a model for polymer solutions and blends that display both an upper and a lower critical solution temperature (UCST, LCST). Using our simple analytic lattice theory along with a fixed parameter set independent of both composition and temperature, we study solutions and blends exhibiting complicated miscibility patterns, including cases in which a UCST is below an LCST, or above. With respect to the former, we examine the conditions under which a so-called hourglass phase diagram may evolve. Where possible we compare directly with experiment, however, we also explore the behaviour of a number of hypothetical solutions and blends. One experimental solution of particular interest comprises star polystyrene (PS) and cyclohexane; in this case we supply what we believe are the only measured pressure-volume-temperature data for a high molecular weight (5.2 × 105 g/mol) star PS.