You can raise the corner with either a Lally column, or with a 4x4 and a 12 ton bottle jack. If you raise with a Lally column you could likely use it as a temp support otherwise frame a temp support for the corner with a temporary column or wall. Then excavate under where the original support column lives to frost depth, drop in a sono tube and fill with concrete. When setting the concrete install hardware for the appropriate simpson style column anchor. When concrete is cured, reassemble original column on foooter with appropriate simpson anchor and remove temporary supports.