Achieving high cell density

Hi all!
I´m currently trying to achieve a very high cell density culture of E.coli, the idea is to use the pioreactor instead of a much bigger one in our lab to test some early hypothesis. In order to do so, I would need at least an OD600 of 30, better if 60+.
So far I only achieved an OD of 10 over 24h but with a clear plateau reached by the cells at 5-6h. Has anyone managed to get much further up? Or is there an intrinsic limit in the set-up, for example due to aeration?
FYI I´m running fed-batch, with feed dosing starting at OD2, and an air pump. I´m also controlling overflow metabolism, acetate and all.
Finally, if anyone has coded an exponential feeding strategy for fed batch it would be grand if you´d share it!

Thanks!

Matteo