S.D. Codified Laws § 61-3-19
The department shall participate in any arrangements for the payment of compensation on the basis of combining an individual's wages and employment covered under this title with the individual's wages and employment covered under the reemployment assistance or unemployment compensation laws of other states which are approved by the United States secretary of labor in consultation with the state reemployment assistance or unemployment compensation agencies as reasonably calculated to assure the prompt and full payment of compensation in the situations and which include provisions for applying the base period of a single state law to a claim involving the combining of an individual's wages and employment covered under two or more state reemployment assistance or unemployment compensation laws, and avoiding the duplicate use of wages and employment by reason of such combining.
SDCL 61-3-19