Someday I'd like to go on and describe systems of notation for ordinals above the Feferman-Schuette ordinal. But I might not get around to it, so here's some stuff for anyone interested - including possibly my future self.
This paper introduced the "Schuette Klammersymbole", which generalize the Veblen hierarchy:
27) Kurt Schuette, Kennzeichnung von Orgnungszahlen durch rekursiv erklaerte Funktionen, Math. Ann 127 (1954), 15-32.
These papers discuss a general concept of "ordinal notation system", which includes the Schuette Klammersymbole and also something called the "n-ary Veblen hierarchy":
28) Anton Setzer, An introduction to well-ordering proofs in Martin- Loef's type theory, in Twenty-Five Years of Constructive Type Theory, eds. G. Sambin and J. Smith, Clarendon Press, Oxford, 1998, pp. 245-263. Also available at http://www.cs.swan.ac.uk/~csetzer/index.html
This paper has a nice expository section on generalizations of the Veblen hierarchy:
29) Jean H. Gallier, What's so special about Kruskal's theorem and the ordinal Gamma_0? A survey of some results in proof theory, sec. 7: A glimpse at Veblen hierarchies, Ann. Pure Appl. Logic 53 (1991), 199-260. Also available at http://www.cis.upenn.edu/~jean/gallier-old-pubs.html
This paper is very useful, since it compares different notations:
30) Larry W. Miller, Normal functions and constructive ordinal notations, J. Symb. Log. 41 (1976), 439-459.
You can get it through JSTOR if you have access to that.
This webpage gives a nice definition of "ordinal notation system" as a coalgebra of a certain functor - nice if you understand categories, that is: