How to handle I global processes in blue-green deployments

I have a global process in an elixir cluster. It subscribes to EventStore, and it is global as I do not
want the event to be received by multiple nodes.

However, we are considering using blue-green deployments in the future.
When rolling out the blue deployment we will have two clusters, each with a global process subscribing to eventstore.

Has anyone encountered a similar problem, and do you have any tips for a good solution?