Is there anyway to proxy or mirror the following Docker registries with my own Private Docker Registry?

• Google Container Registry
• AWS EC2 Container Registry
• Azure Container Registry
• Quay.io
• DockerHub

I want to use a Private Registry to store all Docker Images I need. I want to pull Images without changing the repo/image:tag name when doing a docker pull? For example, with Nexus if I want to do a:

docker pull gcr.io/google_containers/metrics-server-amd64:v0.2.1

I must change the repo name:

docker pull mynexus.mycompany.com/google_containers/metrics-server-amd64:v0.2.1

Is there any docker/kubernetes config that says if someeone does a pull if a gcr.io Image just go to mynexus.mycompany.com instead and use as a pass thru cache.