Cutting-grown potatoes; too many sprouts

I have grown potatoes from cuttings fairly successfully in the past. Reading about spacing, and hoping to improve the crop, I have cut back to soil level some plants (they are all just under a foot high) to give space to the others. However, as many of the stems are from the same cut pieces, I wonder if I have made a big mistake? No sign yet of damage, but I do fear!