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.