It is now commonplace to assume that the production of economically valuable knowledge is central to modern theories of growth and regional development. At the same time, it is also well known that not all knowledge is equal, and that the spatial and temporal distribution of knowledge is highly uneven. Combing insights from Evolutionary Economic Geography (EEG) and Economic Complexity (EC) the primary aim of this paper is to investigate whether more complex knowledge is generated by local of non-local (foreign) firms. From this perspective, a series of recent contributions have highlighted the role of foreign firms in enacting structural transformation, but such an investigation has yet to account for the complexity of the knowledge produced. Exploiting information contained within a recently developed Irish patent database our measure of complexity uses a modified bipartite network to link the technologies produced within regions, to their country of origin i.e. local or nonlocal. Results indicate that the most complex technologies tend to be produced in a few diverse regions. For Ireland, our results indicate that the most complex technologies tend to be produced in a few diverse regions. In addition, we find that the majority of this complex knowledge is generated in technology classes where the share of foreign activity is greater than local firms. Lastly, we generate an entry model to compute the process of complex regional diversification. Here the focus is on how regions develop a comparative advantage in a technological domains more complex than those already present in that region. As such, we focus our attention only on those technologies with the highest complexity values, as these technologies are said to underpin the European Union's Smart Specialisation thesis.