S.D. Codified Laws § 9-43-136
If the assessment originally levied, together with any sum to be paid by the municipality from its general fund or from the proceeds of general obligation bonds, is insufficient to pay the total cost of the improvement, the governing body may assess the additional cost to each lot in the same proportion as provided in the original assessment roll, after public hearing in the same manner as required for the adoption of the original assessment roll. The governing body shall adopt a resolution proposing to increase the special assessment contained in the original special assessment roll by the proportion it determines to be sufficient to pay the total cost of the improvement. The resolution, notice of hearing, and hearing procedures shall be carried out as provided in § 9-43-90. The amount by which each assessment is increased shall be collected by the same procedure and at the same time as the original assessment. However, if any installment of the original assessment has been paid before the levy of the supplemental assessment, the amount of the increase shall be added to the balance unpaid and becomes payable with and as a part of the remaining installments. Interest shall be computed in the same manner as provided for in the original assessment.
SDCL 9-43-136