Casting the Time Stop spell during Time Stop?

I’m wondering what happens when casting time stop during time stop; especially given that the overlapping spells rule exists:

The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don’t combine, however. Instead, the most potent effect–such as the highest bonus–from those castings applies while their durations overlap, or the most recent effect applies if the castings are equally potent and their durations overlap.

My current idea would be the following:

  • Turn 1 of normal time (cast time stop #1)
    • Turn 1 of time stop #1
    • Turn 2 of time stop #1 (cast time stop #2)
      • Turn 1 of time stop #2
      • Turn 2 of time stop #2
    • The rest of turn 1 of time stop #1
  • The rest of turn 1 of normal time.

However, I’m unsure what happens with the overlapping spells rule, especially since the spell doesn’t have a duration besides “Instantaneous”, making me unsure whether the rule applies at all. How would this scenario play out? What happens if you cast time stop mid time stop?