Why do you have so many coming up in a small area? Are they volunteers? If so they could be carrying late blight, which overwinters in tubers. Bad thing since that area was hit so hard last year, so if that is the case keep a very close eye on them.
Each stem coming off of the seed piece is an independent plant so you can pull them off of the seed piece (pretty easily) and replant them. I have done it with potted seed peices (young sprouts), but I don't know how successful you would be pulling a stem out of the ground and replanting it. They may reroot as easily as tomatoes, but maybe not.
If you just want to thin them then pull them out.
Each stem coming off of the seed piece is an independent plant so you can pull them off of the seed piece (pretty easily) and replant them. I have done it with potted seed peices (young sprouts), but I don't know how successful you would be pulling a stem out of the ground and replanting it. They may reroot as easily as tomatoes, but maybe not.
If you just want to thin them then pull them out.
If you had planted large potatoes whole, you would get multiple shoots. The usual recommendation is to plant potatoes that are no bigger than large hen's egg size, and cut up larger potatoes before planting. They should be planted at minimum 12" apart.
If the shoots are not too big, I think you could dig down to the planted potatoes and cut them up with a sturdy knife, then dig up the shoots with as much of the attached roots as possible and replant in new locations, remembering to plant them as deep as they were before. Dusting the cut surfaces with a little garden sulfur might be prudent to prevent spoiling since normally cut surfaces of the potatoes are allowed to dry/are planted in relatively cool soil.
If the shoots are not too big, I think you could dig down to the planted potatoes and cut them up with a sturdy knife, then dig up the shoots with as much of the attached roots as possible and replant in new locations, remembering to plant them as deep as they were before. Dusting the cut surfaces with a little garden sulfur might be prudent to prevent spoiling since normally cut surfaces of the potatoes are allowed to dry/are planted in relatively cool soil.