This paper presents an extension to the Combinatorial Equilibrium Modelling (CEM) design framework. So far, CEM gives the possibility to generate and explore multiple spatial equilibrium solutions in the early conceptual design phase. In addition to the form and force diagrams of graphic statics, CEM introduces a topological diagram, which allows to adjust the connectivity of a spatial strut-and-tie network in equilibrium, its combinatorial inner force state (tension-compression) as well as its metric values (such as element’s length or force magnitudes) in real time. In order to solve more specific design problems within the CEM framework, hence to guide design explorations, constraints-driven adaptation procedures have been developed. This paper describes how these interactive and automatic adaptation methods can be embedded in an overall structural design process containing alternating steps of lateral exploration and vertical adaptation. Moreover, the paper describes how design constraints can be transformed into objectives within non-linear optimization problems and which algorithms can be used to solve them.