JKR herself seems to subscribe to the principles seen in the Terminator films, e.g. that time travel results in a variety of differing timelines upstream, but that these don't generally effect the timeline (butterfly effect style) downstream unless major changes are made. The shorter the jump, and the less interaction you have with other actors, the less impact you're likely to have.
Although the first Terminator film appeared, superficially to obey the rules of the predestination paradox, we later learn that the ability to make informed choices about the future allows time travellers to affect the outcome of events.
Bringing us back to time-turners, while in Prisoner of Azkaban we only see a causal loop (e.g. Hermione and Harry play their parts in an event that has already taken place) we learn from Pottermore that unmoderated use of time travel can result in un-births (e.g. unstable temporal paradoxes)
Any and all time travel within the Potterverse has the potential to result in the user's disappearance therefore a second time loop existing within your own original loop (e.g. caused by the use of a second time-turner by another person) would simply amplify the risk of this happening...
Ellie: Why didn't Harry use the time-turner to save his parents?
JKR: Oh, that's a very good question, that. But it would take us into "Terminator" territory, if you've ever seen the "Terminator"
films... but never mind. Well, the time-turner was a very difficult
invention for me, because it created as many problems as it solved.
And anyone who's read Order of the Phoenix may have noticed that
during the climactic scene in which they chase through the Ministry of
Magic, they shatter all the time-turners, thereby preventing them
using those in the future.
J.K. Rowling's thoughts
I went far too light-heartedly into the
subject of time travel in Harry Potter and the Prisoner of Azkaban.
While I do not regret it (Prisoner of Azkaban is one of my favourite
books in the series), it opened up a vast number of problems for me,
because after all, if wizards could go back and undo problems, where
were my future plots?
I solved the problem to my own satisfaction in stages. Firstly, I had
Dumbledore and Hermione emphasise how dangerous it would be to be seen
in the past, to remind the reader that there might be unforeseen and
dangerous consequences as well as solutions in time travel. Secondly,
I had Hermione give back the only Time-Turner ever to enter Hogwarts.
Thirdly, I smashed all remaining Time-Turners during the battle in the
Department of Mysteries, removing the possibility of reliving even
short periods in the future.