I visit India from LAX frequently and either go via London/Amsterdam or go via the Pacific stopping in Hong Kong or Incheon. I haven't been able to avail of any "free" stopovers despite the airlines making a stop at their hubs. Everytime I have needed to break my journey I have had to book a multi-city itinerary...i.e. LAX-LHR-BLR-LAX and it costs a little more.

Are there any airlines that offer 1 stopover for free outbound or inbound? for example: can I just book a LAX-BLR-LAX on British Airways and ask for the stopover in LHR for the same fare?