You can use enriched media, such as Terrific broth etc., but ultimately, aeration becomes the limiting factor, so  bubbling pure oxygen with a small pore sparger is the key. See Frachon et al., 2006. Appl. Environ. Microbiol. 72, 5225-5231. They achieved up to OD 50-100 (10-20 g/l dry weight) using this approach. A commercial version of the microfermentor battery described in this paper is available from the company  fogale nanotech

We typically reach OD values of 200 and more in our bioprocesses, which are about 50-60 g cell dry weight. As Pierre correctly mentioned, aeration cannot keep pace with fast growing cells. Pure oxygen is one possibility. What we do is running an initial batch phase with low amount of sugar and at the time point of depletion start feeding additional nutrients (a concenetrated solution of key nutrients) by a pump. If you have a bioprocess control system, you can implement a so called "exponential feeding", which will automatically increase the feed rate exponentially. By this, you can force the strain to grow at your imposed specific growth rate. The much lower growth will reduce the demand for oxygen significantly, so cells can grow very high. Check e.g. this one:

Bioprocess Biosyst Eng. 2004 Apr;26(3):147-50. High cell density fed-batch cultivation of Escherichia coli using exponential feeding combined with pH-stat. Kim BS1, Lee SC, Lee SY, Chang YK, Chang HN.

More simple, you can try linear feed with constant feed rate, but here the specific growth will decline continuously and the process takes longer.

I would not use complex media, as they are undefined and probably complicate your protein production and purification.

Controlled feeding of the Carbon source could be the key. this can be achieved by feeding a concentrated carbohydrate (carbon source e.g. glucose) solution in optimal doses so as to maintain the concentration of that carbohydrate to allow growth at the desired concentration. This limiting nutrient can also be a nitrogen source or any other nutrient that might be growth limiting, thats why complex media (with some complex carbon and nitrogen sources) would not be preferred in such conditions as Dr. Christoph Wittmann has suggested

In a batch process you can remove the media+cells when DO becomes a problem and replace the same volume with fresh medium so as to solve the DO problem.

Controlled feeding of the Carbon source could be the key. this can be achieved by feeding a concentrated carbohydrate (carbon source e.g. glucose) solution in optimal doses so as to maintain the concentration of that carbohydrate to allow growth at the desired concentration. This limiting nutrient can also be a nitrogen source or any other nutrient that might be growth limiting, thats why complex media (with some complex carbon and nitrogen sources) would not be preferred in such conditions as Dr. Christoph Wittmann has suggested

In a batch process you can remove the media+cells when DO becomes a problem and replace the same volume with fresh medium so as to solve the DO problem.