Cool! I can see star transfers only when combined with a CM flight. For example, for PTY-LHR:
PTY-CM-LAX-LH-FRA-LH-LHR
PTY-CM-ORD-TK-IST-TK-LHR

But I haven't been able to find anything with multiple Star carriers, or more than 2 transfers.

Interestingly, it seems some fares haven't been completely filed. I can't get intra-US to price unless it includes a CM flight (which seems to open up some semi-interesting possibilities). However, I can get intra-Asia to price without a CM flight (nonstop only).