Brazilian percussionist and composer Ney Rosauro (1952 -) developed the extended cross-grip after encountering problems with tendons in his hands and arms using the Stevens grip for several years. Earlier he had used the Burton grip and the new grip he developed was based on the Burton grip. One of the specific features of the extended cross-grip is the use of an anchoring finger for the outer mallet: It is the ring finger that with its tip presses the outer mallet against the palm creating space between the mallet shafts in the hand. Through this technique the direct contact between the mallet shafts, and the not unusual clicking sound of the Burton grip, are avoided. At larger intervals the grip also uses a technique similar to that of the traditional grip’s method of increasing the spread with thumb and index finger. Ney Rosauro has made very nice and detailed instruction videos that teach his grip at http://www.vicfirth.com/education/keyboard/rosauro.php.
This is what the extended cross-grip looks like at the interval of a fourth.