I plan lots of hay and horse manure on ton top of my gild...so anything else has to be able to handle such treatment... I am thinking maybe some carrot tops to let go to seed, I would be hoping for seedlings.
If there was a plant that would help my asparagus at repelling bugs or provided a mineral or something that I didn't want to grow there (would marygolds be a simple answer?) anyway I would also use that plant for mulch.
My answer for most things is horse manure and either sawdust or hay.
Plants for a future gives this edible description: Young shoots - cooked. Boiled and used as an asparagus substitute (well lookie thar!), they make an excellent vegetable[2, 4, 115] and are widely used in Turkey.
A big part of creating polycultures with nicely partitioned niches is mixing plant architectures and root types. So taller, skinnier plants with tap roots, like cultivated Yarrows, would make good sense as asparagus companions.
Well, I'm late to the party, but I was just researching this question myself, so I thought I'd add my 2 cents.
I have a fairly conventional asparagus patch (though it is planted with a few associates) for high-yielding, large asparagus spears. If that's what you want, go conventional.
But I also have asparagus planted into an ecologically-modeled hedgerow based on a couple of the best wild asparagus patches I know of. The idea here, was to produce low-input, extensive asparagus with more of a "wild" quality (and hopefully the "wild" vigor and disease tolerance.) Also, I was guided by the land, as many of these plants (including asparagus) grow wild in guilds all around me, including in my yard.
I used "improved versions" and cultivated relatives, but the basic wild guild I imitated would be mesic forest-edge, hedgerow or savannah ecology, often in disturbed land with other aggressive plants. Species I've observed around healthy wild asparagus patches (listed from canopy to ground) include Hickory and Prunus species, Elderberry, Hazel, Autumn Olive, Helianthus, Milkweed, Queen Ann's Lace, Chicory, mustards and cresses, and various prairie nitrogen fixers, especially red and white clover. The asparagus is mostly planted in pure clumps surrounded by plants I can "chop and drop" to quickly keep competition down.
I see asparagus growing with asters, carrots and grasses all the time. But the best-looking wild spears, in my experience, come from patches with lots of sun, but without too much grass. It might also be helpful to Google "wild asparagus" and look through the images. Lots of pics of gus with his floral buddies.
Too soon to say weather or not my guild has worked as well as those it copies. Just imitating what I've observed.
Oh, and I've been lurking around Permies for many moons, but this is my first post here.
For what it's worth, my mom's had a fairly conventional asparagus patch going for over 30 years now. It gets regular applications of manure as mulch and she does allow alpine strawberries to grow wherever they show up.