The current debate over what conditions a scheme of mental representation needs to satisfy in order to explain the systematicity of thought is characterized in such a way that (contrary to Fodor, Pylyshyn, and McLaughhn) any complete representational scheme (whether classical or non-classical) can explain the systematicity of thought. Though FPM might reply that non-classical schemes only satisfy these conditions in an unprincipled fashion, this shifts the discussion to less empirical considerations. Recasting the debate, we show that FPM can maintain their objection of unprincipledness only at the price of representational pluralism. Our thesis is that one can maintain representational monism if one uses what we call structured encodings. This will be accomplished by spelling out a representational taxonomy that makes evident what properties need obtain for a given representational scheme to exhibit systematicity effects.