A two-parameter equation of state is a two-parameter corresponding states model. A two-parameter corresponding states model is composed of two scale factor correlations and a reference fluid equation of state. In a two-parameter equation of state the reference equation of state is the two-parameter equation of state itself. If we retain the scale factor correlations derived from a two-parameter equation of state, but replace the two-parameter equation of state with a more accurate pure component equation of state for the reference fluid, we can improve the existing models of equilibrium properties without refitting any model parameters, and without imposing other restrictions as regards to species and mixing rules as already imposed by the two-parameter equation of state. The theory and procedure is outlined in the paper.