Request: Alerts specific to selected pairings

What I'm missing is the option to weigh my alerts. I have a lot of alerts, that I can just look up at my convenience when checking my email.

However what I'd like to see is the option for me to set an alert specific to a certain pairing that will spring up on my phone in a message (and not all the others), so that I know that this is an urgent message in need of my direct attention.

Thanks for considering this.