I have recently seen someone using what looked like a Trello board, but you could 2 way message people from there. 

For context this is for a home service business. 

It was like a central hub where all messages came into one place, and you could assign them to people. 

I'm using ring central right now and zapping text out when needed. You can never see the responses, but it would be sweet if there was a way to set this up. Just like the way you can email out from a task and see the responses to the email in the inside the task comments. 

It looked just like click up which I have been using for a few years now, so I am hoping I can find a solution to implement this into my click up space.

I have look over this big blog post we put together of all the SMS options: https://zapier.com/apps/categories/phone

But didn't find anything there.