We consider leveraging the joint potential of non-orthogonal multiple access (NOMA) and traffic offloading to benefit cell-edge users in multi-cell scenarios. We formulate the edge-driven throughput maximisation problem where both the offloading decision and resource allocation are to be optimised, accounting for the impact of the inter-cell interference on the decoding order in NOMA. The inter-cell interference is not given constants as it is influenced by resource allocation. Therefore the non-orthogonal multiple access (NOMA) decoding order is not known a priori. We explore the problem by decomposing it into two subproblems. By analysis of structural properties, we derive algorithm modules which interact iteratively for reciprocity, forming the overall algorithm. Numerical results show that the proposed scheme considerably improves the celledge throughput, compared with the conventional scheme of orthogonal multiple access without traffic offloading.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.