@Armanda Interesting question, I’m wondering if you’ve experimented with Views at all? This might be helpful to you and an easier workflow -- you can setup views to have certain conditions and filters, so you can show messages in those views if they meet your criteria instead of setting up multiple inboxes for the flow.
For example you could have one that’s setup to be “Waiting on Customer” where you can click to see all the messages waiting on the customer to reply but they would be out of your “Inbox” view that you create that has only the messages that are important to reply to etc.
Does this sound like what you are trying to create? You can definitely do some similar things with Workflows and Inboxes but I’m guessing you are just trying to have a space where you can clearly see what’s waiting on the customer and what is waiting on a response from you -- is that right?
In that case, I think you’ll find Views to be a useful tool here.