This paper examines the contribution of secondary (or gravity) frames to the mitigation of collapse in steel buildings subjected to extreme loading conditions arising from multiple hazards. By considering sidesway and vertical mechanisms as representative of most building collapse modes, this study evaluates the effects of various secondary-frame parameters on the overall building collapse capacity. Given that the beam-to-column joint response typically dominates the behaviour of secondary frames, particular emphasis is given to key connection response characteristics such as stiffness, strength and ductility. The paper starts with a brief description of the probabilistic assessment framework that serves as the basis for the study followed by the assessment of the influence of partially restrained (PR) gravity frames on the collapse capacities of steel structures by means of generalised structural sub-assemblages. Secondary frames are found to provide up to a threefold increase in the sidesway collapse resistance depending on the magnitude of second-order effects. Similarly, the vertical (progressive) collapse capacity is greatly affected by the connection depth versus beam length ratio and the secondary connection strength. A brief discussion on directions for the provision of simplified approaches for the design of secondary frames is presented and illustrated through two case studies involving steel frame buildings subjected to earthquake and blast scenarios, as well as localised fire and blast hazards. This study offers a fundamental step towards the formulation of design and assessment strategies that incorporate secondary systems into a multi-hazard structural evaluation framework.