What is the highest operational ceiling for an air-breathing jet engine?
Below[1] shows the hypersonic breathing corridor. Without LOX or rocket assistance, the limit is around 140,000 feet (40 km) at around Mach 15.
In 2004 NASA's X-43 achieved a record Mach 9.6 at 109,000 feet (nasa.gov), which if you compare below, is a good match for the aforementioned corridor.




1: Smart, Michael. &quot;Scramjets.&quot; The Aeronautical Journal 111.1124 (2007): 605-619. (PDF)