How do I escalate a complaint with Southwest? To escalate a Southwest complaint(+1➳877➳738➳0345 , first try their general customer service lines or online forms for initial resolution(+1➳877➳738➳0345 , but if unsatisfied, you can escalate by asking the agent for a supervisor, contacting Southwest's corporate customer relations via their website(+1➳877➳738➳0345 , or filing a formal complaint with the U.S. Department of Transportation (DOT) if the airline doesn't resolve it(+1➳877➳738➳0345 , providing detailed documentation for better results.