The modelling of polymer melts is significant in finding novel functional materials, which have applications in industrial and consumer plastics, medical devices and microelectronics fabrication. Modelling of complex systems is needed in order to the predict the phase behaviour and, as a result, the properties of these novel materials. We examine the phase behaviour of melt blends of model AB diblock copolymers and B homopolymers with a single functional end on each B chain, leading to the formation of longer diblock copolymers, referred to as ABB block copolymers. Phase behaviour is studied via self-consistent field theory, where particle-particle interactions are decoupled via spatially dependent fields.  The system is modelled paying attention to the reaction favorability parameter, which will determine the amount of ABB product, and subsequently the composition and morphology of the melt. We examine the change in phase behaviour as we increase reaction favorability. We compare the low reaction favorability limit to previously reported non-reactive diblock and homopolymer melt,  and compare the high reaction favorability limit to previously reported diblock copolymer melt with asymmetry in the block lengths. Systems with sufficient ABB diblock product exhibit cylindrical phases, while systems with little ABB diblock product show lamellar phases and ordered-disordered phase coexistence. The distribution of polymer species has been examined for both morphologies. We report the changes in purity and spatial distribution of polymer species for changing reaction parameters, and show the varying phase boundaries of the system. We briefly discuss consequences of these results and comment on future work to be undertaken in further examining the properties of these complex systems.