Simple adjective for "of the size of a proper class"? It's just a wording question: 

How does one tell - by a simple
  adjective - that a collection is "of
  the size of a proper class"?

Their might be several sizes of proper classes, but on the other side, it's not a problem that there are several sizes of infinite/uncountable classes to call all of them "infinite/uncountable".
The context is: How do I have to proceed with "there are finitely many, infinitely many, countably many, uncountably many, weakly inaccessibly many, strongly inaccessibly many, ..." (see Inaccessible Cardinals)?
 A: The word that immediately comes to mind is "large". "Large category", etc. 
Edit: Carl Mummert suggested this one, which I should have remembered myself and which is definitely widely used: "unbounded". "Unboundedly many Woodin cardinals", "unbounded rank", etc. 
It seems to me that the simplest solution would be to say at the outset something like, "for us, 'large' will mean 'proper-class-many'..." or something similar. 
A: I've heard the term "absolutely infinite" used to describe classes of size $\Omega$, the class of all ordinals.
A: I nominate "too big".  
Gerhard "Ask Me About System Design" Paseman, 2011.03.08
A: Proper-class-many.

“We show that if there exist proper class many Woodin cardinals, then the set of reals x for which there is exists an ordinal α with {a ∈ Pω1 (α) | x ∈ L[a]} stationary is countable.”     —Paul Larson, Reals constructible from many countable sets of
  ordinals.

It’s grammatically ugly, but mathematically transparent and unambiguous, and rolls off the tongue reasonably well.  I’ve heard it used by and among set theorists, category theorists, and homotopy theorists, without confusion — I’m pretty sure it’s as widely understood as anything will be for this distinction.
