Is there a modern account of Veblen functions of *several* variables?

After some digging around, I found the following paper:

Kurt Schütte, “Kennzeichnung von Ordnungszahlen durch rekursiv erklärte Funktionen”, Math. Ann. 127 (1954), 15–32 (MR0060556)

The author describes Veblen functions (under a slightly different notation, which he calls “bracket symbol”) in a very clear way, explains how to use them to obtain a constructive system of ordinal notations (or a few closely related systems), and also explains the connection with Ackermann's system which is basically built from Veblen functions of three variables.

It's very well written and the proofs are given in full details. And despite the chronological proximity with Ackermann's paper, Schütte's has a much more “modern” feel to it (were it only for the fact that he starts his ordinals at $0$ and uses notations and terminology that seem more familiar to me). Maybe because the author was younger.

I also noticed Larry Miller's paper, “Normal Functions and Constructive Ordinal Notations”, J. Symbolic Logic 41 (1976), 439–459 (MR0409132), which is useful in that it connects different constructive ordinal notation systems, including Schütte's (hence, indirectly, Veblen functions).

I think the following paper by Buchholz should provide very useful information. http://www.mathematik.uni-muenchen.de/~buchholz/articles/jaegerfestschr_buchholz3.pdf