Adding new results during review process

Yes, yes it is. Just make it clear when you do so the reviewers can review the new additions.

That said, if you think the result merit a new paper, make a new paper, and reference the one under review.

However, while I am an early stage researcher my suggestion is: have a high ethos when publishing. It is way better to have 1 very good paper than 3 weak-related ones. Your objective is to show the world new research, do not fall in the paper-mill trap. Your worth is in the quality, not in the quantity.

In this case you should inform the editor that you have improved results, indicate briefly what they are and ask for his/her advice. It might depend on the state of your original paper's review, of course.

You could also express your desire that it get updated so that it is more complete. Give your reasons as you express them here.

But if you try that and fail it won't reflect badly on you if you publish the updated results separately.