In an AHA moment this morning:

Define EOG, End Of Group, as tilde (~).
EOG is processed, and is to behave analogously to EOF, (End Of File).
Each group of point coordinates ends in a tilde, and each group acts as a CSV file. The txt file of all of the groups of points has multiple CSV file structures, each group separated by tilde in formerly blank line.
Nest EOG While loop, inside EOF While loop.

while ( !f.AtEOF )
{
        While !EOG
        {
             // Process current group set of point coordinates, and save the resulting geometry in a factories array, like in LineWeb.
             // (Later, save and Increment the group name when the factories array is processed into Points or Lines geometry.  Also save the group name as MoI Group names...)
             ...
             PointList.push( point );
             // save PointList in ArrayOfPointlists
             // clear PointList for next group of points.
        }
}
// Process ArrayOfPointsLists into geometry...
...

(~) = tilde = '~' = EOG.

Brian

Is there a pre-existing EOG symbol?
The above code is a very rough draft :-)

(An alternative is to split the .txt of multiple groups of points into 9 individual CSV files, and import each file separately.)