Its best to give the asparagus its own space. It gets tall so would shade any other plants, and the root system is extensive. It is also a heavy feeder, so it would be hard for other plants to compete. You might grow some other plants in the same bed the first year while the asparagus is small. Try some bush beans.
Gardening at 5000 feet elevation, zone 4/5 Northern Utah, Frost free from May 25 to September 8 +/-