Touch tones are also known as DTMF, or dual-tone multi-frequency. There are 4 "low" tones and 4 "high" tones. They combine, two at a time, to create the 16 standard DTMF signals. There's no sequencing involved in * and # - they're just two of the combinations.
The other 4 combinations, which you're not likely to have on your phone, are A, B, C, and D. I have them on an amateur radio Handi-Talkie, where they might be used to control radio repeaters. They were originally intended for military use. See .
You may be thinking of trunk signaling, which I know nothing about.
Jack Hamilton California
Qui vit sans folie n'est pas si sage qu'il croit. François VI, duc de La Rochefoucauld