I've heard of Greater Daemons becoming massively powerful and immense in size (as in mountainous), but could a Greater Daemon become so powerful it could break away from it's Master as a new, lesser, god in it's own right?

I imagine it would take a level of individuality to do this, so, are Greater Daemons capable of such individuality, or are they just pure manifestations of their God and not really individuals at all?

If a GD did 'break away' would it fizzle out of existence, become a rival to it's Master, or have to become a god of some other emotional aspect like other Lesser powers?

If no then same questions for a Daemon Prince...

I could tell some of my ideas, based on some fluff I'm writing, but I'm hoping for some 'untainted' feedback first.