Not sure about the private companies in SD, but the Rural/Metro ambulances that respond with SDFD through the SD Medical Services Enterprise are staffed with one Paramedic and one EMT. Each SDFD fire engine is also staffed with one FF/Paramedic and three FF/EMTs, so any call gets you at least two medics and 4 EMTs.
Up here in LA County, to be considered an ALS unit, you have to have two Paramedics, so thats how most of the FD ambulances and squads are staffed. Assessment units (usually engine companies) can run with only one medic to start ALS care, but a true ALS unit has to be simultaneously dispatched (the assessment medic can cancel them if ALS isn't warranted).
Our department (volunteer) is currently BLS only. We're in the process of trying to add ALS care, most likely through a partnership with a private company. The way we currently work is that all members are expected to get their EMT certification by the end of their probationary period or shortly thereafter (depending on when the class is offered). During weekdays, the ambulance is staffed by the paid fire prevention staff, and the "daytime" volunteer responders (myself included) respond as well in our personal vehicles. On weeknights and weekends, one of the on-duty FF/EMTs (we have 3 crews that rotate weeks and weekends) takes the ambulance home with him/her. Another FF (usually an EMT, but not always) takes the Utility truck (Ford F-350) home with him/her. They both respond to the scene in those vehicles and the other on-duty personnel respond in personal vehicles for EMS calls or to the station for other calls. This gets us, on average, about 8-10 EMTs minimum on every call (and usually more from "off-duty" folks responding).