The jump can be faked by a height variable you can control, depending the design the value can just affect the sprite position and change the collision control to a special state.
While jumping, it should ignore all collision of objects in a level, and start colliding with another level at specific height value if apply, collision body may need to adjust position when stepping on another level.
The way you plan to design the levels will affect the method used for jumping and vice versa, try to make the jumping simple even if levels get too blocky because it may be better for the player.