In this research, we introduce and discuss an extension of max-plus linear systems, called max-plus linear parameter varying systems. In this extension, uncertainty is modelled as a varying parameter, making it possible to leverage non-linearities and non-max-plus terms within the model. Issues arise when the varying parameter is dependent on previous and current states, so-called implicit max-plus linear parameter varying systems. Implicit maxplus linear parameter varying systems are not guaranteed to have a solution. In this work, we introduce some analytical and graph-theoretical methods to analyze the solvability of implicit max-plus linear parameter varying systems. Using these methods, we show that it is not possible to conclude structural solvability for general implicit max-plus linear parameter varying systems. Although, we show that, under mild assumptions, there exist conditions for which the implicit system is solvable. These conditions are explained and applied on an implicit max-plus linear parameter varying model with a state-dependent varying parameter. We illustrate our results with an urban railway network with passenger-dependent dwell time.