Exploring a wide range of relevant design options from the outset is crucial for every sound conceptual design process. Optimization techniques are generally employed to generate well-performing structural design options. However, focusing only on performative criteria may narrow the design brief too early and neglect essential aspects beyond pure performance. In response, this paper introduces a new method for generating structural forms that emphasizes both performance and structural diversity. Applying mixed integer linear programming onto strut- and-tie models, the method employs layout optimization in a new way by (1) generating and modifying custom ground structures and (2) using them to produce systems in static equilibrium that optimize user-balanced sets of custom goals. While the first feature forces a broad exploration of the solution space, the second ensures the generation of only close-to-optimal solutions. Combined, both features provide a new means for generating a trans-topological set of diverse and well-performing designs. The applicability of the method is demonstrated through several case studies. Results show that our formulations allow for the real-time generation of multiple design options, including well-known and uncommon, but no less valid, typologies. Using this approach, designers can move beyond the limitations of established typologies and explore a new variety of structural forms.