Oh, my point with "Do you believe that someone can become more intelligent than they already are?" was genuinely to see if you thought so or not.
I think that people can do things that make them a little bit better at taking IQ tests. Like doing a lot of math will probably make you better at recognizing numeric sequences. Video games might make people a little better at solving spatial matrices. You can increase cortical thickness in some areas with meditation, and the additional focus will give you a cognitive boost. So I think the things we experience matter, and that they can demonstrate some benefits on an IQ score.
But I don't think people can deviate from what they essentially are. Some people are just naturals at speaking or humor, and even if you gave others all the practice in the world, they still wouldn't compare. No memory techniques are going to make me compare to someone who has natural synesthesia. This goes for intelligence too. People can train at certain tasks, and they can thicken certain pathways through effort. But they can't change their genes that code for their myelin sheath coating conductivity. They have almost no control over their Brodmann area morphology, or how many axons are going to be in their corpus callosum. So I don't really buy that environment can make people more intelligent. It only stops people from getting dumber by preventing damage, or it can make people score a little better on IQ tests from "training".