Drawing line from existing one without joining

How can I draw a line from the endpoint of an existing line (snap to grid is on), without the lines being joined?  Joining causes two problems for me:
1. The arrowhead at the end of the existing line moves to the end of the joined line, whereas I want the arrowhead in the middle of the combined line.
2. Even without entering isolation mode the new line gets joined to a line which belong to a group, thus becoming part of that group as well. This defies the use of grouping to create logically connected units.
TIA
Steven

JETalmage wrote:
 ...Worst-of-class Bezier drawing interface. The Pen Tool has absolutely no business affecting pre-existing unselected paths by default. The Pen Tool is not a selection tool, and it violates the entire meaning of something's being selected.
JET
while I agree in principle, on practice when clicking on end points with the pen tool most of the time I do want the paths to join but a lot of other times I do not. So, the best practical solution at least for me would be just holding the Spacebar when clicking on an end point to prevent joining without the need to click away and then drag in place. And they should make this an option in the Preferences for those who want to hold Spacebar only when joining.
The bigger problem is that with overlapping points and edges, Illustrator uses the stacking order and not the selected object when auto joining or adding points which is actually not practical in any case. For example if there are several lines starting at the same point, not the selected but the topmost line will be joined and with overlapping edges adding a point is impossible if the selected edge is not on the top.

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