If your goal is to run each 20lb of solvent over all three columns sequentially, and hit each 10lb column 3x with increasingly LESS saturated solvent, you’re trying to describe a form of counter current extraction.
Tried it a couple of times, works ok, nothing spectacular that we saw.
Decided that the (fastest enabling) plumbing made operation way more complicated, and also made it possible (demonstrated) for the operator to get saturated solvent into the fresh solvent tank.
Automated might work well. correct plumbing involves separate manifolds & inlets for micella vs fresh solvent.
I don’t recall a discussion of this trick specifically for light hydrocarbons, but it has been explored, and you might find insights if you can locate those discussions (try “counter current” and “counter flow”.
I liked percolation, but didn’t spend enough time playing to find the sweet spot.
Edit: Data: potent & efficient lipid infusions via percolation (21 g batches) might work as a starting point.