I've never done this before, but it looks pretty straightforward. The floor at the top of the widened column acts as a tension chord and the one at the bottom goes into compression. You have to design the column to hold the vertical force plus the shear and moment necessary to make the rest of the system work. So it's just beam-column design after you draw out your force diagram.
I'd want to draw a couple of scenarios to make sure I know what happens when there's unbalanced loading, though. I'm guessing it would depend on what your lateral force system looks like. You should just be able to dump the extra diaphram force into the building core or wherever most of your lateral force goes.