Ah, sorry. I misinterpreted your question as to whether it was actually utilized or not, not as to how well it was utilized.
In that sense, there's a substantial genetic contribution (although not complete) and a substantial extremely-early environmental contribution (although also not complete, though more easily influenced, i.e. through First 5 type programs) to general intelligence via brain linkages.
Technically, the plasticity of the brain substantially decreases after childhood, but it never quite disappears - otherwise we wouldn't have memories of any events after puberty ends. However, what this means is that it becomes much more difficult to increase one's brainpower after a certain point in life. Thus if you draw the line for "theoretical maximum intelligence", well... anyone who wasn't raised on Suzuki and flashcards since birth probably would never reach their theoretical maximum intelligence.
It is however possible to train oneself to substantially increase one's intelligence in many aspects: recall/recognition (memory palaces and suchlike), working memory (the dual n-back task, IIRC - there may be others, but those are proprietary and generally marketed as ADHD training therapies), as well as reasoning (solving puzzles and brainteasers and doing proofs and chess problems etc.) So if you're just looking for a substantial increase, rather than Theoretical Maximum Intelligence (TMI? Eh, maybe I should pick a different acronym) it can and probably should be done.
The problem is most obvious in childhood, though. It's frighteningly easy to raise a child's intelligence with a complete disregard for their mental health. Similarly, children who grow up in areas that simply don't value intelligence don't bother with learning, so they end up less "book smart" (although it's arguable whether "street smart" is a complementary or competing form of intelligence).
A similar problem is that of what's valued versus what actually gets taught - for example, the US educational system is supposed to raise creative and competent adults, but it's becoming increasingly clear that it does nothing of the sort. Instead, it raises people who a) know how to navigate complex, age-segregated social situations to the exclusion of all other social situations and b) can memorize information for just long enough so that it survives to be spit back out onto a multiple choice test the next morning. That's how the incentives are aligned, so that's how the children develop.
But I digress.
You can find more of this kind of speculation here. I think about brains too much.