Here's a novelty we can't recommend unless you're willing to take the risk.
Nevertheless, tomatoes and potatoes can be grown on the same plant, their roots
intertwined. Just raise your tomato seedlings as you normally would and then
transplant the seedlings into one-inch holes filled with soil that you have made
in whole seed potatoes (sprouting potatoes or potatoes with "eyes" will do). Lay
the potatoes in a shallow flat filled with soil and wait until the tomato roots
grow through the potatoes and into the soil. When transplanting the tomatoes to
the garden, set the plants (potatoes and all) in one foot deep holes in rich
garden soil. This novelty is certainly a space saver, yielding tomatoes on the
plant above ground and potatoes below. (The potato plant will also send up
vines, of course.) The chief drawback is that potatoes can transmit several
diseases to tomatoes, and vice versa, which is the reason potato fields on farms
are always widely separated from tomato fields. We had no such trouble though,
luckily. If you have an out of the way area available you may want to
experiment. Many such experiments have been made with tomato plants. At North
Carolina State University, for example, tomatoes were grafted on tobacco plant
roots. The result was a tomato with high nicotine content! One of the earliest
experiments with tomatoes, in 1919, produced a tomato eggplant chimera having
characteristics of both parents on the same branch.