Booking an international flight on multiple airlines with separate itineraries can be risky. The potential for problems can far outweigh the savings.
Elizabeth Marini found this out the hard way. Her parents purchased her a ticket on TAP Portugal flying out of John F. Kennedy International Airport. She then booked her connecting flight from Boston to JFK on a separate itinerary on Delta Air Lines.
This became the precursor for her distressing trip. “Why you should never, ever book your flights this way”