Hi @yehoshooa fried -- Cam from the Intercom Support Engineering team here! 

That certainly sounds like it might be useful integration for some companies! To be perfectly honest, given how the Intercom Calling ibeta] functions and the various rules, regulations, and restrictions around this capability I’m not to sure if it’s going to be possible to build an integration that does this at present, but I’m sure you have an idea in mind as to how you might achieve this so don’t let me dissuade you from trying! 

This article gives a general rundown on the different types of Apps that can be built and how they function (it sounds like you’d be looking to create a custom Public Inbox App), and our Dev Docs - here - walk through how to get started build an App/integration, and this page dives into building Inbox Apps more specifically. 

Hope these details help! Let me know if you have any follow-up questions

hi Cam G thanks for u kindly response , i will check the article and will let u know if i have any more qwestions, 
thanks again!