You can stack tires and grow potatoes that way, it might increase the calories per square foot
Or, you can plant Sunchoke Sunflowers that make tubers that taste like potatoes and they reproduce on their own. Plant them one time, and they make others underground with those tubers. Leave a few tubers the first time, and they will reproduce like crazy.
The problem with regular potatoes is, you need potato slips every year to grow more potatoes. In a SHTF situation, you can't buy or order more slips, so you have no more potatoes. The potato like Sunflower tubers, keep growing forever. Use the tubers exactly like a potato.