Multi-Arm, Multi-Stage (MAMS) clinical trial designs allow for multiple therapies to be compared across a spectrum of clinical trial phases. MAMS designs can be categorized into several overarching design groups, including adaptive designs (AD) and multi-arm (MA) designs. Factorial clinical trials designs represent an additional group of designs which can provide increased efficiency relative to fixed, traditional designs. In this work, we explore design choices associated with Factorial Adaptive Multi-Arm Multi-Stage (FAST) designs, which represent the combination of factorial and MAMS designs. This category of trial can potentially offer benefits similar to both MAMS and factorial designs. This work is motivated by a proposed clinical trial under development.