There is a lot of talk about companion planting. First, define companion planting as planting two or more species that co-exist to mutual benefit and do so with overlapping root zones. Anything planted as a companion to tomato should be a moderate feeder and have a relatively small leaf area. You would not for example plant squash beside tomato because it is both a heavy feeder and has a massive leaf surface area. The same logic applies to corn since it is a heavy feeder and requires full sunlight.
A different scenario entirely is presented by interplanting tomato and cabbage. On first thought it sounds pretty good because you would plant the cabbage up to 2 months before the tomatoes and you would have harvested the cabbage before the tomatoes reach their main production point. So long as small type cabbage plants are used, it can be made to work fairly well. The problem I encounter is that various caterpillers are attracted to the combination and I wind up using poisons to control the bugs. That means the combination did not meet the definition of companion planting since there was no mutual benefit. I would still use this method if space is an issue but define it as interplanting, not companion planting.
A much better companion for tomato to me is onions. I have used bunching onions between the tomato plants to some effect. The onions do not compete seriously with the tomato for nutrients and the combination seems to reduce somewhat the number of pests on the tomatoes. If the tomatoes sprawl, the onions may have a tough time but by winter they get enough light to grow and by the next spring are in good shape to eat.
My last example is my personal favorite method of companion planting. It is to plant tomatoes and use marigolds as companion plants. I use nemagone marigolds which make a small flower and grow 2 to 3 feet high. I usually put 4 or more marigolds around one tomato. Eventually, the tomato suppresses the marigolds but they manage to peek out of the foliage cover most of the season. The marigolds reduce problems with bugs and seem to help a bit with foliage diseases. Several people have reported serious problems from spider mites with this combination.
I know there are many other companion crops that would work. I have not tried many possible combinations since space is not a problem for me and I just grow enough plants to make a crop no matter what hits them.