the evolution of the human brain size
I assume, you mean by "producing DNA" Neanderthals had larger brains than us. Basically, this is possible and generally, brain size correlates with body size. What you may ask here is: Can our brain size to body size ratio increase? Probably yes... I can't think of a reason, why not?

But please please be aware of that intelligence, does not have to correlate with brain size. e.g. elephants and humans. There may be some limits of the smallest possible brain size for certain mental tasks and skills. But wiring and plasticity is probably more important than the bulk size.