I'm a personal trainer so I am constantly texting my clients with appointment times or just to check up (I have my gyms name after each client's name so all I have to do is search my gym name and they all pop up). So one thing that I think that could be helpful for some people would be a folder with different conversations.

the main screen could have all the convos like it does now but once you swipe (or whatever gesture or case may be) you are swtiched to another screen that has specific conversations that the user has grouped together.

any ways just a thought! love the app regardless