Yes there is
When you make a deep cut (the only ones where you need bandageing) you need to bandage half of the the centers of the first shell. Two opposed centers must NOT be bandaged.
2x2 ---> 3x3 bandaged with three centers around a corners. Two opposed centers are never both bandaged.
Pentultimate ---> Megaminx bandaged with 6 centers: 1 and the 5 around it. Two opposed centers are never unbandaged this way, and it is easy to bandage it as a whole because it's 'clean'. If you took randomly half of the centers you'd have to bandage different pieces in different places. With the 5 around 1 method, all the bandages are made in one place.
Good luck with your designs !