We only do raised beds, due to the acidity of the ground. And corn doesn't do too well in a Finnish climate, not much of it being grown here. But I'll be sure to look into what I can grow together, onions and salads seem like a good combo at least. I don't think I want to leave the parsnip in the ground over winter though, somehow I think that a few months of -20 deg C won't do it good.It might work, but parsnips are a long season crop, however, you'd be pulling out the onions and greens, followed by the carrots. Then you could leave the parsnips. Here in the states, we let them winter over, and they are super sweet in the spring. I'd suggest that you try a small plot this way, and see what works for you. I've always planted onion sets with lettuce with excellent results. You might want to check out some sites regarding companion planting. Some crops benefit each other, while others have a negative impact on each other. Too exhaustive a list for me to go into it here. Onion sets, lettuce, carrots, spinach, and radish are a great combination. And it looks so pretty while it's growing with the multiple textures and colors. If you do a mixed planting, be sure to not plant so thickly, and start harvesting at the "baby" stage b/c everything grows so fast.
An other great mixed crop is potatoes and corn. You could plant a row of potatoes between every 2 rows of corn, then leave a path, then do a repeat. Just be sure to get those potatoes mulched deeply. Corn will be happy with mulch as well. Tomatoes surrounded by lettuce. Cukes with fern leaf dill. Cabbage, tomatoes, or broccoli in the asparagus patch. The options are endless. If you can have your garden covered with growing green stuff and a heavy mulch where you are not growing stuff, the weeds are minimal. Weeds are opportunistic, taking root where ever there is bare soil. If the soil is never bare, what's that poor weed seed to do???
BTW, my first garden was a 4' x 4' plot in such compacted soil/gravel that i could only dig down 4". I did not harvest ANYTHING that would be considered edible!