The functionalisation of two-dimensional materials is key to modify their properties and facilitate assembly into functional devices. Here, new reactions have been proposed to modify crystalline two-dimensional carbon nitrides of polytriazine imide structure. Both amine alkylation and aryl-nitrene-based reactions have been explored computationally and with exploratory synthetic trials. The approach illustrates that alkylation is unfavourable, particularly at basal-plane sites. In contrast, while initial trial reactions were inconclusive, the radical-addition of nitrenes is shown to be energetically favourable, with a preference for functionalising sheet edges to minimise steric effects.