"Supplemental oxygen" refers to getting extra oxygen to help a person breathe better when they need it, usually given through a mask or tubes. Full definition
If your doctor says that your child is stable enough to fly with supplemental oxygen, you will have to make arrangements with the airline at least 24 hours before your flight. (caringforkids.cps.ca)
These poor guys require true intensive care and monitoring, often requiring supplemental oxygen therapy, serious pain control, (multiple) surgeries, and temporary feeding tubes. (preventivevet.com)
However, if the dog has trouble breathing, more intensive treatment such as supplemental oxygen is necessary. (raisingspot.com)