For three points Wellman Chamberlin of the National Geographic Society invented the “trimetric” projection.
W. Chamberlin, 1947, The Round Earth on Flat Paper, Washington D.C., Nat. Geogr. Soc.
His diagram is pretty self explanatory. The arcs of distance from the three points chosen to bound the area do not meet exactly, but rather form a small curvilinear triangle. The centroid of this triangle is used as the position of the graticule intersection. This would appear to be a least squares solution, but is not so described in the literature.