Not a whole lot of possibilities - should be accepted?
Quite colloquial, but the meaning is definitely sound. I would report and suggest.
What is wrong with "Not very many possibilities"
Nothing, I would suppose. Reported it.
It is now accepted (2014-06-02).
does not look English..
I'd say: "not too many possibilities " or "not so many ways"
It seems fine to me, or at least no better or worse than your suggestions (they all seem like they needs a "There are" or something before them). Maybe it's a regional/dialectal difference.
I'm with you. "Not very many possibilities" sounds just fine to my Australian ear. "Not so many..." sounds American to me, but certainly not wrong or weird.
Listen three times and never hear the "en" at the end. Typical