If you are jumping a lot in two lessons a week, that is plenty. No more jumping. Ground poles if you need to work on your eye.
OP, I mean this sincerely. You have a very cute, nice horse who seems game. Enjoy him for what he is and who knows where he will take you. The more often you jump him, the shorter the period of time he stays sound is, and the less fun you will get to have.
There are a number of people on this board who have “done horses” for longer than you have been alive. Most of us really are here to support one another and try to solve problems (and find cheap Tailored Sportsman). If you come asking for suggestions on how to improve your horse’s jumping technique or what you need to do to be able to jump higher with specific questions, you will get a wealth of knowledge.