On the ShippingDocker.com site there's a video (and matching tutorial) posted showing you how to use Docker to test with multiple PHP versions with relatively little difficulty. In this case they're not testing the frontend of the application, they're running its unit tests.

[This is a] quick video on running PHP unit tests against different versions of PHP using Docker. [We'll] cover unit testing with PHP.

They start with an example of using the pywatch tool to do the testing without Docker, automatically executing the tests when something changes. This has the limitation of only being able to use your current, local version of PHP. They then shift over to the Docker side of things and show how to run the same pywatch command inside a container of your choosing, tagging it with the PHP version and making it easy to switch between them in the future.