Indoor multi-functional sports arenas are a complex building type. Integration of the (multi-) functional space and of the large-span structure of the roof mainly determines the overall geometry of the building, and is one of the most challenging phases of the design. Several interdisciplinary numeric assessments and numerous solutions with diverse geometries (rather than just several specific types) should be considered to make informed design decisions. To support the design exploration in the early design stage for multi-functional arenas, this paper proposes a design process that is composed of a flexible parametric model, a framework of interdisciplinary assessment criteria, and multi-objective optimization (MOO) with post-process tools. The parametric model is defined based on the basic spatial composition of arenas and is flexible to provide a broader design space, including diverse solutions with three frequently-used structural types. The framework of assessment criteria includes indicators of viewing quality for spectators, acoustics, and structures, which can evaluate the design in different aspects. Based on certain assessment criteria, the MOO can be used to search for good designs in the broader space, and the post-process tools facilitate the designer to analyse the results. Two typical arenas (the Barclay Centre and the O2 Arena) are selected as real case studies to demonstrate the proposed process and assess the capacity. Results of the case studies validate the efficacy of the process and the necessity of the broader design space to include diverse solutions with multiple structural types.