It sounds like you my have potato onions. I tried them, and did not have good luck, but I think I put them in super rich soil and a raised bed. I've found multiplying onions seem to like our own soil here: clay mixed with compost. Adding sand to the clay - it really depends on the type of sand. Play sand, or fine sand and clay makes cement. Course sand works quite well but I'd add more clay. The generally "accepted" (meaning, it seems to work and is popular right now) is 1/3 amendment to 2/3 clay.
Both your shallot and multiplying onions are considered perennial. Although they get divided, I've found you don't need to rotate them. You can keep them in the same bed but every few years you can lift, divide and add lots of yummy home compost. This is working for me well for a different kind of multiplying onion (topsets) and leeks.

Are these the spring onions? I planted them in the fall, they set seed a while back and are putting out green tops again. I'll dig one up and see. Can we plant onions again for a fall crop, I am enjoying my red onions, my leeks are doing great. Not very much experience with onions, but lovin it.

girlgroupgirl, I'll try that mix and see what happens, My first experience with onions so I have already figured it will not be perfect.

Mark

organic gardenhag, no, not spring onions - a different onion that is considered a "walking" onion and it will not set seed.
Leeks will perennialize by division and will also multiply from seed if you let some do their thing!

I can't offer any advice, but I planted some walking/multiplier onion sets for the first time at the end of February. Eight came up, and 6 have survived the heat. Apparently they go kind of dormant in hot weather, so just keeping them alive is a big deal. They don't look that sexy at this point (merely like green onions), but I feel confident now that they'll easily survive into the fall.

Hope everyone else who plants these has some success too.