From what I have read, shaking the carboy, the aquarium pump, and the mix-stir all get you to about 8 ppm dissolved O2. That is as good as it gets with air. That is good for most ale yeasts in beers up to 1.060 to 1.070 or so.
To get to the 10 ppm or more that is recommended for lager yeast, you need have an O2 system. That would also be good for a 1.100 beer.
What do I have? A mix-stir, a an aquarium pump, and an O2 system. I have been known to shake the carboy also.