Was having a discussion with a friend about the longest nonstop flights and this topic just came up...what would be the longest 3 continuous segments back to the origin would be with flights currently in service?

The most I've gotten so far is

DFW-SYD 8,578 mi on QF
SYD-DOH 7,688 mi on QR
DOH-DFW 7,932 mi on QR
Total 24,197 mi

Thinking there should be an itinerary with more...