This paper focuses on a singularity exhibited by most dense fluids in the (alpha, P) plane (where alpha denotes the isobaric expansivity and P, the pressure): for a given fluid, nearly all isothermal curves share a common intersection point. In this paper, we test the capacity of a series of equations of state to model this little-known phenomenon. Equations of state that can be written as the sum of an attractive and a repulsive term are first considered. As a result, equations of state involving a Carnahan-Starling repulsive term always predict the aforementioned crossing point contrary to equations of state involving a classical Van der Waals repulsive term. Quantitatively, the Carnahan-Starling-Van der Waals (CS-VdW) equation of state and the Carnahan-Starling-Soave-Redlich-Kwong (CS-SRK) equation of state both lead to satisfactory results. In addition, some pitfalls of the Carnahan-Starling-Peng-Robinson (CS-PR) equation of state are identified which justifies that this model cannot represent dense-fluid behaviors. The Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state is then tested. The obtained results are more extremely satisfactory when compared to the CS-vdW equation of state. Finally, a general criterion that must be verified by equations of state in order to predict isotherm crossings is proposed and illustrated. (C) 2012 Elsevier B.V. All rights reserved.