Single Application Load Balancer for multiple EKS clusters

I have two clusters - one named staging and the other production and I want to introduce a new service that will be deployed to both. I want to be able to access the service in each environment/cluster using different URLs - something like the two below.

• new-service-staging.mydomain.com
• new-service-production.mydomain.com

I also have an AWS Load Balancer Controller as an ingress controller deployed on both clusters, that create a new application load balancer when a new Ingress resource is created

Is there any way that I can utilize a single Application Load Balancer (ALB) on AWS that will direct traffic to each cluster based on the requested URL?

I know I can set up multiple target groups and set up different rules for different hosts under the ALB, so I can have multiple ingresses point to the same ALB - but from my understanding, this is only the case for Ingresses within the same cluster, as again from what I got from the documentation the ALB that is created is tagged and assigned to a specific cluster

So I was wondering is there really a way that I can use a single ALB to direct traffic to multiple clusters?