Basically I have a limited amount of space and a really short growing season. Gardening season here starts in April (for cool weather stuff, weather cooperating) and the main season is in end of May; it ends in September-November (depending on weather).

I'd like to maximize my space and extend growing season by doing companion planting.

I have some ideas, but I honestly have no clue what I'm doing; they're guesses at best.

beans/okra with 'short crops' (leafy green stuff and root veggies)

corn with melon/squash (this IS NOT three sisters)

root veggies with fruiting crops (by fruiting crops I mean eggplant, tomato, peppers).

I figured this would be a natural since they both need potassium and phosphorus as their main nutrients; however would planting them together cause them to compete for food?

I could also use advice on what to plant with brassicas since they're a difficult crop group to pair with other veggies. Somebody suggested members of the onion family goes well with them but I don't know. By brassicas I mean 'cole crops' (turnips, kohlrabi, cauliflower, broccoli, green cabbage, red cabbage, chinese cabbage, etc.)