below is the code snippet on how to update a field in sharepoint list which contains multiple chioce value
using(SPWeb oWebsite = SPContext.Current.Site.AllWebs["Site_Name"])
{
SPList oList = oWebsite.Lists["listname"];
SPListItem oListItem = oList.Items[0];
oListItem["columnname"] = "choice1;#chioce2;#chioce3"
oListItem.Update();
}