The first page of this article covers how to run two versions of macOS on a Mac that has a second APFS volume.

However, if you aren't in the APFS world yet, you will need to partition the main hard drive into two separate drives and then install macOS Catalina on one and the other version of MacOS on the other.

How to install a second macOS on a Partition

If you need to create a partition you will need to wipe your Mac, so as we said above, make sure you make a backup.

The simplest way to create your partition is to do the following:

  1. Boot macOS into Recovery mode (start up your Mac and hold down the Command and R keys until you see an Apple logo or spinning globe).
  2. Once in Recovery mode, use Disk Utility to wipe the main hard drive and split it into two partitions.
  3. Now recover your Time Machine backup into that partition. Remember, you won't be able to recover a backup based on a newer version of macOS than the one you want to be using on this partition.
  4. Alternatively, you could use the Install option in Recovery to install whichever version of macOS you wish to run on to the main partition.
  5. Now it's time to install the other version of macOS in partition 2. Follow the steps here to install a second version of macOS, or the beta of the new version of macOS, on to the second partition.