I have different tacks depending on how I'm growing them 405.

In open ground, like I suspect is your method, I learned to hill them as the season progressed. Meaning using a rake -from the opposite side of the row- to pull dirt up close and high around the foliage growth, and then doing the same from the other side, thereby providing more dirt for more taters to develop in. If you have a tiller and enough space between the rows(a future planning consideration) just till the paths first(which also knocks off some weeding:).

Before you do that though, feel around and find some early potatoes and snitch a few nice sized ones. The plant will recover(but be gentle:).

As to mulch: I don't see why you couldn't do with potatoes as described above. I'm moving toward the Ruth Stout method of gardening where pretty much everything is mulched. Part of Stouts deal with potatoes was that once you got your mulch built up to a depth of say 9 inches(which takes a few years(unless you have a good cheap source of hay-which I wish I did), she'd simply pull back the mulch with a rake and drop some potatoes on the ground in the spring and cover them up to a depth which still allowed the foliage to work its way through, followed by increasing the mulch depth, little by little, in conjunction with the top growth. Which I think answers your question.

To my understanding, that method allows the roots to REALLY spread out, producing far more tubers, while also allowing EASY access if you want to snitching a few ANY TIME during the season. I'm a few tons of hay removed from the benefits of that program, but I'll get there.

The other way I grow potatoes is with old tires. Primarily because we have a great deal of land that's too hard on the equipment to till(subsurface slate). I add more mulch every time I add another tire to keep up with the vertical growth and as the years have progressed, I've gotten more potatoes per stack(I suspect because the surface level hummus is building up nicely). It seems the leaves I add simply give the potatoes a place in the dark to grow while awaiting their turn to rot. [Besides thinking I'm crazy(I'm sure) people are generally delighted when I stop and ask if I can take away their leaves. Since they do the raking I generally bring back goodies which has its benefits too, the following spring or fall.]

That's the beautiful thing about the no till/mulch method, it actually improves the biological life of the soil while cutting down on weeding(it's a whole lot easier weeding mulch than say roots anchored in clay). I'm liking it even though I don't mind weeding because it's improving our results.

I may followup via PM with more later if I find something useful after I (inevitably)crack some books. I'm in the early stages of learning this gig. Several years of intense failure has it's benefits, LOL.

hope that helps(& I didn't bore you too much).

to an lush harvest

Btw ... Thank You so much for asking ... I just realized an unintended plan developed during the writing. A clarification if you will. It's very coool, how plans come together, lol, thanks!