Jumps are definitely possible, and I think it's more a function of learning the "game" of the mcat than it is packing your brain with more info.
Just make sure you're not overdoing it with regards to practice tests.
For a month after my TPR course, I took every aamc test I could find. I reached a high of 37/36 halfway through, but as my test date neared I began dropping, ultimately scoring a 33 on my last two which extended to my actual test. Really would've loved those FOUR POINTS though...
Point is, increases are def. possible, but so are point drops. Don't wear yourself out prematurely by stressing over/pounding out practice tests...
Pace yourself.