- If Cappy gives a boost to Mario, it doesn't count as a jump, so by throwing Cappy and bouncing on him, it allows Mario to "jump", allow him to do a cap dive to cover ground
- When Mario is unconscious at Bonneton and The Forgotten Isles, Mario will eventually get up without actually jumping
- When Mario captured an enemy, their jump actions do not count, so it's possible to reach high places with them
- In Fossil Falls, there is a 2D section that requires jumping by default to reach the boss area, therefore it would seem impossible, but there is a trampoline that makes the T-rex bounce super high, allowing Mario to escape the dino and reach Madame Broode without initiating a jump action
- On The Forgotten Isles, Cappy would have been captured by Klepto, but Mario cannot reach the air without jumping if he's alone. The trick is to go high up before the area where Klepto will snatch Cappy away, and defeat him at his home turf before he did any stealing
- In Bowser's second battle, there are sometimes where Bowser would create rings of fire while Mario's in Bowser's top-hat, but by rolling and attacking, he can avoid Bowser's attacks.
- Talking to NPCs normally would initiate the jump counter, presumably because there is a split millisecond where Mario is jumping, so to solve this, Mario ground pounds before the NPC and talk to them in mid-air since Mario is technically in his "jump" state, but is not actually jumping
- Finally, in the Moon's Core, Mario wakes up automatically as a regular jump, so it would seem impossible to not jump, were it not for the second player. Yes, Cappy can bounce Mario so that he wakes up without jumping, and continuing from there.
By doing this, talking to Toadette will show that Mario's jump counter is zero, so it is indeed possible to complete this game without Mario jumping.