Between the [strike]ferns[/strike] raspberries.

I've begun the clean up of  my front yard raspberry patch by tying the canes up to stakes.
There are three rows of plants, with roughly 3 foot between plants and 6 feet between rows, mostly because that's how they spread.
This leaves space in between  that's begging to be used.
The thing is, most advice here on permies suggests that the only thing raspberries are happy sharing space with is mulch, so I was thinking I would plop down boxes(2x2 raised beds) full of mulch in the row between each plant.
In that mulch , I would grow something shallow rooted that likes mulch, like potatoes.

This is a thing I've done next to trees and fruit bushes, but not as tightly as I'm considering here.

I suspect that the companion plants raspberries prefer may be climate dependent. Mine seem very happy with stinging nettles. Given that raspberries have a relatively shallow root run and like it cool, dampish, but not water logged, I wonder whether comfrey might actually be a good companion, or another deep rooting self mulching plant.
As regards potatoes, I could see that working quite well, especially on the outer edges of the raspberry patch. the act of digging the potatoes could trim the raspberry runners for you too. I think of potatoes as liking it quite sunny, but this is probably climate dependent too!

Comfrey has been mentioned positively and negatively as a good companion.
There is already some a few feet away, along with daylillies and tree seedlings.
Nettles, I have tried,  and I kept hurting myself!
Gobo might do well in a bottomless container.
Maybe dwarf sunchokes.
Rhubarb could take the mulch, make more mulch and give a yield.

I am happlessly compelled to build things, but maybe I shouldn't do that here, and just mulch.
Maybe add a single comfrey or elderberry in between raspberry plants, for mulch and compost ing acceleration.

Well, at least one of the transplants is unlike to make it.
My wife had some some rabbit bedding/poop and suggested mulching them with it.

I was a little extra smitten and swoony over that!

Anyways they got a deep soak, and a bunch if mulch.

I first thought your topic was ferns and raspberries, because that is how I have them growing!  raspberries growing up out of a patch of Ostrich ferns.  They get along well, and you can eat the fiddleheads in spring.  It is tricky getting to the berries without breaking too many ferns, though.  I put in some steppingstones.