Can Mojave be installed on separate APFS volume under Catalina? I am running Catalina as my primary OS but am finding that I'd still like to run some 32-bit apps. Is it possible to create a new AFFS volume, install Mojave and simply run a dual-boot system?

Things that did not work:
I have created a new APFS volume, but I cannot figure how to make it bootable.

I was able to download an official build of Mojave but cannot get to the install screen because of an error message telling me This copy of the “Install macOS” application is too old to be opened on this version of macOS.
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


Click on this link which will open the Mac App Store on the Mojave page.
Click Get.
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. 
Wait while the macOS downloads - it may take a while.
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


Open "Disk Utility"
Click "View" -> "Show All Devices" (⌘2)
Click on "Container disk1" and "Add APFS Volume..."
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


Reboot your computer, hold down the Option key (⌥) before the Apple logo appears
Choose the USB media (Mojave installer)
Click "Reinstall macOS" once the "macOS Utilities" screen appears
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".