Synthetic Controls - Comparing Two Treatments All of the literature on synthetic control groups examines situations where 1 or more units receive a treatment and are compared to non-treated units. I am wondering if there is any statistical or mathematical reason why these techniques cant be applied to a situation where both treated and "control" units receive some treatment, but the treatment differs? For example, some units receive treatment A and the others receive treatment B. Is this viable?

As usual, @dimitriy gives good advice. But I have a different approach: you can use the synthetic interventions estimator in this case. It was designed to solve this specific problem! I'm working on what I believe to be an improvement of the SI estimator, but this does as you want (what if treatment A happened in B, what if B happened in A...) for each unit.
