Adsorption fixed bed models are of paramount importance in chemical and environmental engineering research. Although the related literature is rich, the vast majority of models employed are either phenomenological, based on chemical reaction kinetics, or limited to systems that obey simple equilibrium isotherms (favorable, unfavorable, linear, and rectangular) combined to linear driving force (LDF) for the solid-phase mass transfer kinetics and ideal plug flow. This paper complements the existing studies by presenting and analyzing a versatile nondimensional fixed bed model equipped with diffusion-based mass transfer kinetics and nonideal flow terms and adapted to deal with S-shaped (sigmoidal) isotherms. A discussion is conducted on the rather unusual fixed bed dynamics produced by systems that follow S-shaped isotherms, a subject which has been rarely and nonsystematically discussed in the related literature. Thus, this study aims at providing better understanding of the interactions of S-shaped isotherms, mass transfer, and axial dispersion on the shape of adsorption fixed bed breakthrough curves and comes to clarify and complement previously published results, especially on the unexplored effects of the isotherms' inflection point on the breakthrough curves.