Clion: Build and run in existing Docker instance

Clion has support for running in a Docker container. My understanding is that this is going to spin up a new container and build everything in there. Is there a way to have Clion attach to an existing container? 

I understand that it would be possible to just publish a container as an image and then build in that, but this does not satisfy my requirements. I fundamentally am going to need to be able to specify the container name, have Clion attach to it, and then build