Does illustrator not allow you to continue a path with the pen tool when the path is completed?

[Evelyn___]

 Trying to add a straight line here, but adding points on the path doesn't allow me to create a new line. Every point I hover over shows me a minus sign.

[Monika Gause]

There can only be 2 path segments be meeting at one anchor point.

What is your actual goal? We need to find a different way.

[Jacob Bugge]

Sulinn,

In order to also avoid the ugly spike in any case, you can switch to Round Join in any case.

Starting with what you have, one simple possibility is to create a straight path with the Line Segment Tool between the Anchor Points you wish to connect, then Group.

Smart Guides are your friends, telling you when you are within snapping distance.

[Jacob Bugge]

You can get round the issue with a single path in the following adaptation of an ancient way, also starting with what you have, and also with the help of Smart Guides:

1) Click one of the Anchor Points you wish to connect with the Scissors Tool to open the path, then Click (the topmost one) with the Pen Tool to continue the path;

2) Still with the Pen Tool Click an empty spot near the other Anchor Point you wish to connect, then Click the (bottommost) first Anchor Point to close the path;

Now the line between the two Anchor Points is off at one end, so:

3) Switch to the Direct Selection Tool and Click an empty spot, then ClicDrag the off end of the line to snap it to the first Anchor Point.

[Kurt Gold]

In the general Illustrator preferences there is an option called "Disable Auto Add/Delete".

Turn this option on.