One example of this is Los Angeles-Delhi. Probably possible with existing planes but would require cargo or passenger limits, which would make the route not profitable. No American airline is interested, given the connections available elsewhere, and Air India's (they've expressed interest in this pair before) habit of running routes at big losses will probably start to reduce now that they're privately owned. Airlines are perfectly happy to add more hops to your trip.

If there was a supersonic LAX-Singapore (I doubt India would allow supersonic planes), at least the longest leg of the trip is mostly over ocean, supersonic, and the Singapore-DEL flight is just a normal one.