You can Add to a type path by clicking its end point with the pen tool and continuing to draw the line.
To join it with a separate path you can copy the type path by "direct selecting" it with the hollow arrow tool, copying and pasting (paste in place or simple paste). This converts it back to a simple path that can be joined with any other path. Then you can convert it to a type path again.
Note: Make sure you select ONLY the path, not the text, when copying the path. Here are fool-proof steps:
- Switching to outline mode (Cmd/Ctl+Y).
- Choose Direct Select tool (A).
- Hold "Option/Alt" to convert to "Group Select" tool and click just the line (this will select the full path, but not the text).
You might want to create a new layer then paste the path "in-place" (Cmd/Ctl+F). This way you can work on the new line without affecting the original type path.