The Maggio system was established because Louis Maggio had sustained an injury which prevented him from playing any other system. He tried a pucker instead of a buzz or a curl.
This pucker allowed the bad tissue to vibrate in a different point and he could play.
Maggio claimed that the pucker allowed him to not only play higher but also longer because the pucker made a cushion between the mouthpiece and the teeth.
Carlton MacBeth was the main teacher of this method and he wrote a book which is sadly out of print. The last one I saw for sale was 895 dollars.
This embouchure is elusive for some players. The pucker is so different from what they used before that they lose control and sound quality. Others do well.
In this system you cushion the lips by extending them or puckering ( like a monkey ).
In fact their T-shirts are a closeup of a monkey forming the embouchure.
This puckering enables the players to overcome physical malformations.
It also lets the player play for an extended time in the upper register.
I DO advise people who can not play other embouchures because of injury or serious dental malformations to TRY Maggio.