So my Google-fu didn't show any references on this. I'm studying an obscure set theory (ML, a variation on NF with proper classes) and it seems to not deal well with the standard definitions of ordinal number. I'm wondering if anyone knows of any references (if they exist) to approaches besides the von Neumann or Frege-Russel ones.

(The specific problems are that the von Neumann ordinals are unstratified, so even ones that exist can't seem to measure wellorders [the usual recursion fails]. The Frege-Russel version works, but the numbers can't generally be guaranteed to be sets since quantifiers in set abstraction must be restricted to sets, and some sets have subclasses which are proper classes [so the usual meaning of "wellorder", among other things, would need to be altered].)