Allow Custom Pipeline builds to be queued

So for context - we have a custom master branch pipeline that occurs each time that a pull request is merged into our master branch. In this build, once all the tests pass and all the other checks are successful we tag the commit with a version number - this certifies to our team that this commit is good to proceed to the next stage in our deployment. This provides us with certainty that each and every change we make is stable, but as you might have guessed this means that we can only process one pull request at a time.

If we merge more than one PR into master then our tagging system risks getting confused - which creates work for our team to clean up. Is there a way to allow builds using a custom pipeline to queue up rather than all running at once? Or should we rethink our entire tagging system?