In this study, an equilibrium theory solution for a binary system subject to a specific subclass of generalized bi-Langmuir isotherm is derived. This solution provides a thorough understanding for the type of isotherm investigated, which exhibits several interesting features. Depending on initial and feed compositions, the order of breakthrough and desorption changes at frontal analysis conditions, and a changing impact of component 1 (from competitive to cooperative) on the adsorption behavior of component 2 can be observed at displacement conditions. Furthermore, the equilibrium theory solution includes some rare transitions, such as semishock transitions with multiple shock and wave parts. Due to its interesting behavior, this isotherm is able to accurately describe an experimental system investigated in the context of the delta-shock phenomenon. With the aid of the derived equilibrium theory solution, it was possible to identify several types of transitions and intermediate states, and to fit isotherm parameters to experimental elution profiles. The interesting behavior accounted for by this type of isotherm, and its ability to describe a specific and peculiar experimental system, which had previously been misinterpreted, may motivate the future investigation of the entire class of generalized bi-Langmuir isotherms.