Design-based methods have recently been developed as a way to analyze data for impact evaluations of interventions, programs, and policies. The estimators are derived using the building blocks of experimental designs with minimal assumptions, and have important advantages over traditional model-based impact methods. This report extends the design-based theory for the single treatment-control group design to designs with multiple research groups. It discusses how design-based estimators found in the literature need to be modified for multi-armed designs when comparing pairs of research groups to each other. It also discusses multiple comparison adjustments when conducting hypothesis tests across pairwise contrasts to identify the most effective interventions. Finally, it discusses the complex assumptions required to identify and estimate the complier average causal effect (CACE) parameter for multi-armed designs.