Other than a few system alerts it’s not possible unless the developers specifically provide a sound within the app which gets played back for notifications. In short Not user changeable.
Thanks.
Wait, what exactly are you talking about. I change sounds on my phone through the root file system all the time. You can even change the dial tone sound and even the alert when siri pops up. You can add sounds to most apps too.
I’m guessing you’re jail broken?
Well yes but we are in the jailbreak and ios hacks forum so...