BA now operates a number of the old Concorde flight numbers (BA1, notably) as business-class only flights on an A318 from London City to JFK, with a fuel stop (and customs and immigration pre-clearance at Shannon) on the westbound flight (due to London City's short runway). I do wonder if Concorde would be more profitable nowadays following that example, seating a very small number in standard business lie-flat seats. (Though maybe one doesn't actually need actual flat seats, given flights are all under four hours.)