Is there anyway to set a concurrency limit for the number of branch deployments we can have running at any one time?

Do you mean the number of runs across all branch deployments? Or the total number of branch deployments?

The number of jobs running across branch deployments. We run an integration test on opening a PR that creates a branch deployment on which a testing job gets triggered. Ideally we would like to be able to limit the number of testing jobs across different branch deployments to ensure that we stay within available compute resources.

@Dagster Bot issue Configure run concurrency limits across branch deployments

Created issue at: https://github.com/dagster-io/dagster/issues/14940