Double shine

In the words of FreddyP from GameFAQs,

"Double, triple, quadruple, and so on shine is just shine, jump, shine, jump, shine, etc

''Same for both Fox and Falco, and can be done forever. The important thing is that the next shine has to be done before Fox/Falco leaves the ground after jumping from the previous shine, which is 4 frames for Fox and 6 for Falco. You need insanely fast reflexes to do them, and very very few people can consistently do even a double shine in a match."''

The double shine is also refered to as the triple shine.