This article explains the effects of Jump proficiency and how to raise it in Super Mario RPG Remake. It also covers what Jump proficiency is and the maximum number of jumps.
What is Jump Proficiency?
Jump Damage Increases

There is a proficiency system exclusive to Mario's special move "Jump," where the damage of Jump increases according to the number of times Jump is used.
Powerful for Dealing High Damage with Low FP

As you increase proficiency, it may deal more damage than Mario's other special moves. A major advantage is that Jump's FP consumption is very low at "3".
If You Want to Master Jump, Also Increase Magic Attack Power
Since Jump is a special move, its damage increases as you raise magic attack power. If you want to further increase Jump's damage, consciously work on improving your magic attack power.
How to Raise Jump Proficiency
Strengthens Based on the Number of Times Jump is Used

The damage of Mario's special move "Jump" is strengthened according to the number of times it is used.
Mushroom Way is Recommended for Raising Proficiency
In Mushroom Way, there is "Mario's Pad" right next door where you can stay for free, allowing you to quickly recover FP consumed by Jump while raising proficiency.
Jump Proficiency Cap
*High Possibility of a Cap Being Set
The cap for Jump strengthening is currently under investigation. However, since a cap was set in the original version, it is highly likely that a cap is also set in this remake.