Extend the edge for the jump.

I have the problem that when reaching the end of the platform. I need it to extend a few more pixels so that I can make a better jump. How could I achieve that without modifying the player's collision?

That's called "coyote time". You can use a manual timer that starts as soon as the player starts falling, and allow the jump code to execute during that time.

Thanks, I'll do more research now.