Reindexing thread

Note sure if possible, but I would like to know if I can reindex a thread to open it deeper.

Let me explain it better: A thread was opened and I needed to remove the part from the lathe. Figured out that I need to make the thread deeper. How can I clamp it again and still open the thread on the same spot? I understand that I can do this by switching the Z axis, but how can I check when the threading tool is on the thread track?

Issue solved.
Made another part(s). Too much trouble in setting the tool.

I have done this in the past. Here is how.

Set up the G76 as before, with the same parameters and let it run in air.
On the spring-pass stop the spindle (override to zero)
Put the work loosely back in the chuck and rotate it in until the threading tool engages properly.
Then you can press "stop" and change the G76 parameters to re-cut the thread.