This paper presents a new methodology for cost- and carbon-optimal generation of multi-storey building designs. The methodology features algorithms for automatic optimised design of concrete, steel, and timber frames; established as well as novel decking technologies; and foundation options. Applying the methodology, we illustrate the potential carbon and cost savings unlocked by well-informed early-stage design decisions by means of two test cases: a simple rectangular building and another with more complex geometry. We show that the impact of early-stage design decisions such as column grid, site, frame material, and decking choice have much larger emission saving potential than the choice between optimisation objectives.