When we have caisson jobs, we provide the geotech with reactions at each caisson. Then the geotech takes that information, along with his geotechnical investigation data to model each of the caissons in a program (usually L-Pile). He then provides us with shear, moment, and displacement curves for each caisson. With the shear and moment diagram for each caisson, we'll typically design one set of reinforcing for each different diameter caisson. It's pretty uncommon to have more than one diameter for lateral caissons, though.
Be sure to specify to the geotech if your grade beams are intended to restrain the caissons. Many will automatically assume they do if grade beams exist. You don't always want to have that much moment transfer through the caisson/grade beam joint, so just make sure that your assumption is made clear to the geotech.