i know 30 something cast on's and have never heard of a triple cast on.
there is a cast on called a doubled long tail (it makes a thicker, wavier edge than normal cast on.) and it is made with 3 strands of yarn.
Measure out the amount needed for a standard long tail (i like to use 3.5 times width (a 20 inch hat or sweater back would require a 3.5 x 20 or 70-to 75 inches of tail) then double it--(make the tail 2 strands of yarn each 70 to 75 inches long!
make a slip knot (or not) with single strand
hold single strand over index, and double strand over thumb and make a 'normal' long tail. (It's done the same way as a normal long tail, but its not normal--the double strand makes a thick wavy edge)
for more cast on idea's check out my 4 part tutorial on blogs that starts here
there are links at the end of each part to the next..
if you find directions to a triple cast on--please let me know.. i would love to add it to my collections.
(there is also a 3 color/3 strand of yarn cast on that creates a braided sort of edge.. but i have never seen it done in a single color.. (there are links to the latvian braided cast on's on page 4 of tutorial)