My asparagus is in a raised bed in order to have good drainage, so I cannot really say first hand how well asparagus generally does in wet soil, but I do know that when grown in poorly drained soil, asparagus can rot off right at the soil line. I'll try to find a link that describes the disease. I think it is a fungal thing. While you sometimes see "wild aspargus" (which I assume is just one of the old O-P varieties that has naturalized) growing in and along bar ditches that obviously serve to drain water during periods of heavy rainfall, the plant breeders have done so much breeding work with asparagus that today's male hybrids are not at all like the old varieties. They are a bit more persnickety and like to have well-drained soil, and don't tolerate poorly-drained soil as well as some of the old O-P types seem to.

The raised bed where I grow the asparagus is at the low end of my sloping garden, and the pathways and grade level soil at that end of the garden had standing water in it for a good 2 months this year, and possibly a couple of weeks longer than that. I am pretty sure the asparagus would not have survived sitting in water like that for so long. In May, we had 24.5" of rain, with almost a foot of that in one day, and I watched the asparagus carefully because it sits in such a low spot. While the path uphill from it held a ton of water for weeks and weeks (the raised bed's border kinda served as a dam), the asparagus never looked unhappy. That asparagus bed does sit about 14" above the pathway and that is, obviously, by design in order to ensure that our asparagus lives and produces for decades.

I probably wouldn't try it in a very wet location, although you might be able to build a tall raised bed above grade level where that wet spot is and grow it there. It would just depend on whether the excess moisture wicks up into the raised bed.

I cannot think of many edibles that like really wet soil. Probably water cress, and then there's some of the exotic stuff like Taro. Some people say the brassicas grow well in wet soil, but I am assuming they mean wet sandy or sandy loam soil and not wet clay, because back in our early days here before we had built many raised beds and before the soil had been amended year after year, I had brassicas rot off right at the soil line when we had especially wet weather. If you like to grow mint, it does tolerate exceptionally wet soil. Cranberries like boggy soil. Oh, and rice does too.

We have a little river of water that flows underneath our garden from the neighbor's property which sits quite a bit higher than a garden. It isn't a problem most years, but in a wet year, I can hit that river of water 8 or 10" down when digging. It is one of the reasons we have raised beds. I don't know if it is an underground spring or if it is from runoff, but either way, I didn't know it was there when I chose that spot for the garden (it was a drought year so there was no river of water underground), but I learned more and more about it with every wet year we had. I had intended to only have part of the garden be raised beds and part of it be grade level, but over the years, we've built more raised beds to work around that underground river of water (I wish it was there in drought years, but it isn't!) in the wet years. Now that front garden is about 75% raised beds, and eventually it will be 100% raised beds. If I learned anything in this very wet spring/early summer, it was that even the very sandy soil at the far north end (the downhill end) of the garden can stay too wet in a wet year, so I'll probably work on building more raised beds down there this winter for next year (unless it rains all winter long).

Hope this helps.

Now, here's a link than mentions the problem caused by asparagus being grown in wet soil. It isn't the article I remember, but it says that a planting of asparagus shouldn't be within 4' of a low water table. Ooops. My asparagus probably is....but the raised bed saves it.

Asparagus

Sigh, I don't know where to put the asparagus. Lovage is supposed to like wet soil, but I planted some next to this bed and it managed to dry out and die during a hot spell. I couldn't even get blanket flowers to grow there. I could continue to put straw bales there and grow something above ground. Going to plant daikon radish there. Wonder if they can break through for better drainage. DH said to try it. We will see in spring.