The problem is: Berlin can't. There is not much free space for new construction in Berlin proper, with the exception of "Nachverdichtung" such as you propose with apartments over parking lots - and these have the downside that they are horribly expensive, simply because it costs potential developers a lot of money to acquire the land!
The solution would be to build out internet connectivity and public transport in the suburbs in Brandenburg so that employers don't all concentrate in Berlin.