I have a running multi-container kubernetes pod and I want to add another docker container to this running pod instead of deleting and creating the pod from scratch.
When you make changes to your pod and deploy them, the replication controller will delete the pod and recreate it with the new configuration - that's how Kubernetes works.
If you're worried about downtime, you can set your Replicas to 5 for example, and enable Rolling Update. This way the pods will be restarted one by one.