Does Kubernetes support persistent volumes shared between multiple nodes in a cluster?
Yes it does. What you're looking for is to set your AccessMode to ReadWriteMany.Note that not all Volume Plugins provide ReadWriteMany.
Multiple pods might be reading/writing to the Volume plugin at the same time. If a node/pod were to restart, you would still have access to the volume.
To get a full list of what which Volume Plugin supports that, refer to the official documentation.