public void RemovePoint( 
   int index
)

// assume a multiPoint has been built from 4 points
// the modified multiPoint will have the first point removed and the last point moved

// use the builderEx constructors which don't need to run on the MCT.
MultipointBuilderEx builderEx = new MultipointBuilderEx(multipoint);
// remove the first point
builderEx.RemovePoint(0);
// modify the coordinates of the last point
var ptEx = builderEx.GetPoint(builderEx.PointCount - 1);
builderEx.RemovePoint(builderEx.PointCount - 1);

var newPtEx = MapPointBuilderEx.CreateMapPoint(ptEx.X + 1.0, ptEx.Y + 2.0);
builderEx.AddPoint(newPtEx);
Multipoint modifiedMultiPointEx = builderEx.ToGeometry() as Multipoint;