I posted the process of creating a bed for a double row of potatoes a couple weeks ago and, after a little research, I plan to plant companions in the bed tomorrow. Plants from the cabbage family seem to grow well with potatoes, so most of my cold weather veggies can be planted in the middle of the potato rows. This includes cabbage, kale, and broccoli. In warmer weather beans and corn both do well with potatoes. Perhaps I will plant beans here as the cabage family is finishing off in late spring.
Some plants help to repel Colorado Potato Beetles. These include tansy, nasturtium, coriander, catnip, flax, and lamium. I already have nasturtium seeds and will sow them directly into the soil after the danger of frost has passed. Nasturtiums also repel a wide range of other pests. One possible problem is that they prefer poor soil. I have not ammended this bed with any compost or manure so hopefully it will be poor enough for them.
If I plant beans and corn here at the same time as the nasturtium the vines, which generally stay under 2′ tall, should grow up the corn. Eventually the beans may over take them but that is ok. Nasturtium leaves and flowers are edible and delicious in salads. I may add some flax, catnip, or coriander as well but I do not have a definate plan to do so. I do not really use coriander in my cooking, nor do I have a cat or care for catnip tea. Flax interests me but I know there is not the space for much. Still, I would like to try my hands at making linen and do use flaxseed oil. These are all things to consider when planting your companions. Each plant should be useful to you as well as groupings being planted to benefit each other.
You can also interplant crops that will grow quickly and be finished before potato digging time. Radishes, scallions, spinach, and leaf lettuce can all be good choices for this. Since I am not living on the property to be looking after such crops I do not plan to do this but if you are planting in the yard where you live and want the most productive space possible give it a try. one nice thing with potatoes is that they store well in place so if a longer standing crop is planted over them you can just wait to dig the potatoes. This does leave them in a place where root pests can get at the though so keep that in mind when planting.
Some plants should not be planted near or after one another due to similar nutrient needs or similar disease and pest problems. For potatoes avoid planting after or before tomatoes, eggplant and peppers. A few others are rumored to increase the risk of blight as well so avoid cucumbers, raspberries, sunflowers, pumpkin, squash (both summer and winter) and tomatoes for this reason. Tomatoes and potatoes seem to be especially good as passing pests and diseases back and forth so absolutely avoid planting them near each other or planting one after the other.