Apple - Can Mojave be installed on separate APFS volume under Catalina?

Yes, this is definitely possible. I just created this exact setup with macOS Catalina (10.15.1) as the "main" OS, and a separate macOS Mojave (10.14.6) installation in an APFS Volume (same disk, same container).

Follow these steps:

Step 1

Download "Install macOS Mojave" archive

1. Click on this link which will open the Mac App Store on the Mojave page.
2. Click Get.
3. The Software Update window up from System Preferences will open showing the latest version of Mojave. Confirm that you want to download the software, you'll also see a warning that you are downloading an older version of the OS, ignore it.
4. Wait while the macOS downloads - it may take a while.
5. Once it’s downloaded DO NOT click on Open - you don't want to install it yet.

(from https://www.macworld.co.uk/how-to/mac-software/downgrade-macos-3581872/)

Step 2

Create APFS volume

1. Open "Disk Utility"
2. Click "View" -> "Show All Devices" (⌘2)
3. Click on "Container disk1" and "Add APFS Volume..."
4. Enter Mojave in "Name" (leave "Format" as "APFS" - I also did not specify any size options)

Step 3

Create bootable installation media for Mojave

Follow the official instructions at How to create a bootable installer for macOS

In short summarized form:

Format a min 16GB USB stick using Mac OS Extended, call it boot, then run:

sudo /Applications/Install\ macOS\ Mojave.app/Contents/Resources/createinstallmedia --volume /Volumes/boot

Replace /Applications with ~/Downloads in case the installer is still in your Downloads folder.

Step 4

Boot from install media, and install to Mojave volume

1. Reboot your computer, hold down the Option key (⌥) before the Apple logo appears
2. Choose the USB media (Mojave installer)
3. Click "Reinstall macOS" once the "macOS Utilities" screen appears
4. Select the Mojave volume when asked where to install

Once the installation is finished, you can use the "Startup Disk" program to set you main Catalina installation as the default. When you want to boot Mojave, just restart the computer, hold ⌥, and select "Mojave".

Someone asked in a comment here if macOS can be installed without first creating a separate installation media / usb boot disk.

Yes you can, provided your macOS installer is not in the same volume where you want to install macOS too.

Here's how:

1. Let's assume you have two hard disks or partitions named Catalina and Mojave respectively.

2. You have macOS Catalina on /Volume/Catalina.

3. You have downloaded and copied the macOS Mojave installer into a directory called 'OS' and hence the installer is at /Volume/Catalina/OS.

4. Using Disk Utility, you have formatted /Volume/Mojave as either HFS+ (best for older hard disks) or APFS (recommended if you have a SSD drive).

5. Now boot into macOS Recovery mode - press the cmd ⌘ + R keys when switching on your Mac and don't let go till you see the Apple logo

6. In recovery, open the Terminal and run this command:

   $ /Volume/Catalina/OS/Install\ macOS\ Mojave.app/Contents/Resources/startosinstall --volume /Volume/Mojave

Note: If you have disabled SIP, you can run the command without booting into recovery (see the comments for more details).

Apple has moved the old MacOS installers around since this article was published. I found the answer on appleinsider here: https://appleinsider.com/articles/19/11/23/how-to-get-an-old-macos-installer-from-apple

The article also provides links to earlier versions as well.

The link to get Mojave is:

https://itunes.apple.com/us/app/macos-mojave/id1398502828?ls=1&mt=12