2D Top-Down Platforming like Mario and Luigi: Super Star Saga

Hey, I have a few months of experience with unity can have been able to learn A LOT. I've created several small games ranging from 3D FPS games to 2D sidescroller games. My current endeavour has me stuck: How can I create a 2D Top Down game that allows the player to jump on platforms, enemies, etc. Here is an example of what I am aiming for: https://www.youtube.com/watch?v=ZmqE8qqyh_A

I understand the concept of using the Z axis to achieve something like this jump, but here's the dilema: I want to keep this game 2D, and with 2D colliders, z-order does not affect collision. an object with a z pos of -1 can collide with an object of 324 z pos.

I've tried using the ignoreCollision method and changing the Y position with the jump to jump on a pillar. However, when i walk off the edge of the pillar, the player does fall down behind the pillar but keeps walking (because moving up and down is based upon y pos).

Does anyone know how his can be achieved with having to use 3D? I'm not looking for free code, but a good explanation of how this can be done is much appreciated. Coming from a background in writing and animation, i feel like I'm not approaching this correctly.

(also the combat in mind is more link legend of Zelda, which i know how to do, not a turn based RPG like Mario & Luigi: SSS)