Currently, it's not possible to perform two deployment builds to the same environment at the same time.
When you try this, the following message will show up:
This pipeline was paused because another pipeline was deploying to Test.

The build will stay paused in this state, and a "resume" button will show up.
If there are deployment branch restrictions active, the resume button will stay grayed out, and will not allow you to proceed with the deployment.

Steps to reproduce:

1. Add the following configuration on your yml:

pipelines:
  default:
     - step:
        script:
         - echo a
     - step:
        deployment: test
        script: 
          - echo a
  pull-requests:
     '**':
     - step:
             script:
              - echo a
     - step:
             deployment: test
             script: 
               - echo a

2 . Go to your repo settings > Deployments > This happens for any environment, but in this case, for testing purposes, select the "test" environment >Add any branch to the "Branches allowed to deploy to Test:" textbox

3 . Create a new branch, and add a commit to it. This commit should trigger a build As soon as the commit is added, before the build that gets triggered by the commit ends, go to the pull requests page and create a new PR for the created branch

4 . This will trigger two builds. The build that finishes first will be able to deploy to the environment whereas the other build will get blocked with the following error:
This pipeline was paused because another pipeline was deploying to <environment>.

This is expected. However, even after the deployment ends, the "Resume" button will never allow you to deploy to the Test environment, and this is the issue here.

A workaround for this is to remove any deployment branch restrictions you may have on your repo. The "Resume" button will not be greyed out anymore.