Previously I have posted about a diverse set of layered strongly correlated electron materials which exhibit a non-classical magnetoresistance. Specifically, the magnetoresistance can be largest (smallest) when the current and magnetic field are parallel (perpendicular).
Michael Smith has just published a nice paper Anomalous interlayer magnetoresistance in bilayer crystals which considers a simple concrete model that exhibits such behaviour. The key physics is that in alternating layers the conducting chains are perpendicular to each other. This does occur in some organic charge transfer salts, as mentioned in footnote 1 of the paper.