Partial upgrade to Catalina

You can install Catalina on a separate disk or partition and continue to use Mojave as you always have. Read Upgrading macOS without fear - Apple Community for the procedure.

You can perform the converse also: restore Mojave onto a separate disk or partition, then install Catalina over your existing system. Boot Mojave when you need it. Read Restore a disk using Disk Utility on Mac - Apple Support for that procedure.

When you download and launch the Catalina installer, it will ask you to select an installation location. It's identical to the picture shown in the User Tip above—it just says macOS Catalina instead of Mojave.

You must click the "Show All Disks" button. Choose the new, empty volume you just created. Don't forget to do that, otherwise the installer will overwrite your existing Mojave installation.

When the Mac restarts, it will boot the Catalina partition. That's normal. Your Mojave system will remain unaltered.

To choose which operating system you want to load when you start your iMac, just press and hold an option key while starting it with the power button on the back or restarting it from the  menu.

Just in case you overlooked it, Apple's recommendation to back up your Mac shouldn't be considered optional, even if your Mac were working perfectly fine and you weren't contemplating upgrading macOS just yet. Why? Even though what you propose is 100% correct, suppose you make the simple mistake of not selecting the desired installation location. What then? Or, suppose by sheer happenstance that's when your Mac decides to go belly up and simply won't start at all.

Another reason for reiterating those instructions is that despite repeated recommendations from Apple and everyone else, people continue to overlook that fundamental requirement. Then, when upgrading macOS they find out old and unsupported programs no longer work, or something else unexpected happens, and their Mac world comes crumbling down. Misery ensues. Understandably angry, they blame Apple for their own lack of due diligence. It happens every year around this time, and will continue to happen as long as Apple releases macOS upgrades in the fall.

Don't be one of them. Back up your Mac.