I am trying to come up with a list of vegetables that like to have their stems buried, like tomatoes and potatoes. The plan is to build up my soil over a long period of time, while at the same time doing a modified french intensive style garden. So, while the plants are growing, I plan to add more soil, and plants, and soil, and plants, and so on. This way, I build up my soil, while at the same time making a productive plot.

I plan on starting with potatoes in the cooler season, and as they grow, bury the stems, which encourages tuber development. Then as the season gets warmer, add tomatoes, as they grow, bury their stems, which encourages root development for the tomatoes, while encouraging more tuber growth for the potatoes, etc.

So, I am looking for other vegetables that can be grown in this environment. Celery comes to mind.

Any other suggestions?

With potatoes, you should bury stems because tubers are set above the original tuber along new stems. I would never plant in succession plants of the same plant family sharing the same pests and diseases.