Customising Notification Lists

At the moment the Notification list isn't editable and only notifies you of incoming messages for messaging channels. 

I'd love the ability to see ticket notifications based on different intents such as requesting an order cancellation or order amendment, which agents need to pick up instantly too. 

We do have our ticket priorities, views and SLA's set up to prioritise these tickets within the interface, but we feel for agent efficiency it would be great for each business to be able to organise based on intents and not based on channel. 

Any further advice, ideas or thoughts on how others are currently organising top priority tickets alongside messaging tickets to ensure these are getting instant responses would be great :) 

Thank you!