Software is becoming an integral part of a range of products and services performing vital functions in all sectors of economic and social activity. In such softwareintensive systems, software applications are required to interact, in a seamless way, with other software components, devices, sensors, even humans. The complexity involved in building the software components that will be deployed in such systems in not so much on the "size" of their code but on the number and intricacy on the interactions in which they will be involved, what in [6] we have called social complexity.From an algebraic point of view, social complexity raises new challenges with respect to the more established physiological complexity, i.e. the fact that a complex whole can be understood as a composition of its parts. The basic difference is that it does not make sense to see software-intensive systems as being compositions, in an algebraic sense, of simpler components. There is not a notion of whole to which the parts contribute but, rather, a number of autonomous entities that interact with each other through external connectors. This is why it is so important to put the notion of interaction at the centre of research in software-intensive system modelling, and to support methods and languages that separate interaction concerns from computational ones. In the past, we developed Abstract. We extend the theory of (co-)spans as a means of providing an algebraic approach to complex interactions as they arise in software-intensive systems. In order to make interconnections independent of the nature of components involved, interaction protocols are formalised not in terms of morphisms (i.e. part-of relationships) but a generalised notion of (co-)span in which the arms are structured morphisms -the head (the glue of the protocol) and the hands (the interfaces of the protocol) belong to different categories, the category of glues being coordinated over that of the interfaces. The proposed generalization sheds some additional light into adjunctions in bicategories, namely on the factorisation of left adjoint 2-sided enrichments.