how many harmonics?

By the way, about 3rd octave:
how many harmonics can you sound after bottom D? (That means, keeping all tone holes closed)

With my Rose (Fred) flute, I can reach
High D
high A
3rd octave D
3rd octave F
3rd octave A
and, sometimes, 4th octave D.

I wonder wether it’s related to the thickness of the body, because my other flutes, thicker, can’t reach so many harmonics.