You are not permitted to exceed 16 segments for a voluntary reroute. An involuntary reroute may involve exceeding 16 segments, and that has happened to me on multiple occasions. I didn't mention it in my post above because the context is voluntary reroutes. Note that even with an involuntary rereoute, exceeding 16 segments can cause problems in reissuing the ticket. There are various ways to work around such problems, of course.