Lakatos’s methodology of scientific research programmes centres around series of theories, with little regard to the role of models in theory construction. Modifying it to incorporate model-groups, clusters of developmental models that are intended to become new theories, provides a description of the model dynamics within the search for physics beyond the standard model. At the moment, there is no evidence for BSM physics, despite a concerted search effort especially focused around the standard model account of electroweak symmetry breaking. Using (...) the framework provided by Lakatosian research programmes, we can capture the way the periphery of a model-group changes as the available parameter space shrinks, while its central tenets remain untouched by unfavourable experimental findings. By way of motivation, I provide two case studies of model-groups that offer alternative mechanisms for electroweak symmetry breaking: supersymmetry and composite-Higgs models. Both of these model-groups are under pressure from the discovery of the Higgs boson, yet they have both been active research projects in the years after the Higgs discovery. However, a proper assessment of the progress of an ongoing research programme is impossible through a purely Lakatosian lens, so I propose replacing it with Laudan’s problem-solving account, which provides ongoing assessment, while offering normative guidance concerning the pursuit-worthiness of research programmes. My incorporation of model-groups into Lakatosian research programmes captures the developments of two attempts to expand our physical description of the world, and Laudan’s problem-solving rationality allows us to assess their pursuit-worthiness. (shrink)