As well as standard *A RTW there are other options.
Eg1 an SQ only RTW with side ticket LAX-ORD-JFK
Eg2 4 corners RTW (SQ/NZ/VS/BD) with side ticket LAX-ORD-LAX (SIN stopover cannot be on way to/from LAX)
Eg3 LH fare to Europe with side ticket LAX-ORD (again SIN stopover cannot be on way to/from LAX)