Can a character with physics behavior pass through another object and stand above it like a platform character?
Sure by enable-disable those behavior at right moment.
It's better to disable physics collisions with the platform object, but keep the Physics behavior enabled.
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Generally speaking, the logic for a jump through platform is to disable the solid (immovable, for physics) behavior for the platform when the player sprite's y position is below the platform's y position, and enable when on top.