Electrodynamic bearings can guide rotating objects without contact and active control means. Consequently, their performance relies on passive phenomena that require specific models to be predicted. In the case of electrodynamic thrust bearings, early models involved assumptions on the rotor axial kinematics. This precludes their use for predicting the bearing behavior in dynamic conditions, which is critical when studying stability aspects. Other models require numerically solving of Faraday's current law and the rotor equation of motion to obtain the dynamics of the bearing, thereby excluding a fast identification of its stability properties. Recently, a parametric model without these kinematic assumptions was derived. It consists in a linear state-space representation that allows studying the dynamic performance of electrodynamic thrust bearings using conventional system analysis tools. However, this model links up the rotor displacement to the currents in a winding with only two phases. This paper introduces a model free of this limitation, allowing to consider bearings with a higher number of phases, an improved copper usage, and potentially increased performance. Furthermore, the proposed model directly links up the rotor displacement to the force and torque exerted by the thrust bearing without requiring to solve for the currents. This also minimizes the number of state-space equations and model parameters. Finally, in addition to the modeling aspects, a set of bearing topologies that have not been explored yet and can be studied using the proposed model is introduced.