I took a quick look at the SD statutes and did not see anything that would preclude you from carrying open and another concealed (except in a courthouse) as long as you had a permit to carry concealed.
In WA if you have a concealed permit you can carry open, or concealed, and loaded in a vehicle.
Without a permit you cannot carry loaded or concealed in a vehicle, SD looks similar.
Basically I look at our WA CPL as a permit to carry loaded in a Vehicle, as well as a permit to carry concealed. Looks like SD sees things the same way.