How do I increase the amount a player can stand over an edge before falling off?

The default detection for whether a player should fall off an edge isn’t forgiving enough for my purposes.

I want players to be able to walk on narrow beams without the player falling with the beam between their legs and for them to not fall off when their camera is just a pixel over the edge.

Do I need to program my own Player:Move() function?

Using invisible boundaries is not what I am asking for.