To create a predictive method for an associative equation of state, the parameters of a specific associative group should be transferrable among molecules. The hydroxyl group, one of the most common associative groups, is a good starting point for this development. On the basis of a previous study where a modified version of the Cubic Plus Association (CPA) EoS was shown to present accurate results for alkanols with almost constant association parameters, this work addresses branched, secondary alcohols, 1,omega-alkanediols, and glycerol to evaluate how CPA can handle steric hindrances and the presence of more than one hydroxyl group. The pure component properties studied here are vapor pressure, saturated liquid density, saturated liquid isobaric heat capacity, and heat of vaporization. Some VLE, LLE, and GLE of binary systems are also analyzed, showing how the modifications affect the description of binary/multicomponent systems. Some systems containing petroleum fluids are also analyzed.