feminine, masculine and... ?

I have been thinking about the possibility for a grammar with pronouns to
have genders for masculine and feminine for people and animals according to
natural sex and a third category which serves optionally either for the
traditional neuter or for such nouns representing a person or animal where the
gender need not or can not be named.
Hardly an original thought, probably...
I do have trouble finding an appropriate name for this third gender. Just
calling it neuter would not really point out the additional possibility of
use which you dont usually have in natural languages, at least not in those
of west european origin.
Englisch is not my native language, is there already a word describing
what I want?
If not, would "masculine, feminine, unspecified" sound terribly strange in
the ear of a native speaker?

              Thank you for your comments

              Cavallero

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