Running Catalina and Mojave simultaneously

I am running Catalina 10.15.2.

I recently bought from IRIS a scanning mouse only to find that, although it will work with earlier Mac OS, it is not compatible with Catalina and “it is questionable whether it ever will be.“ I could return the mouse for a refund but would really like to put it to good use. I’m therefore looking at ways of partitioning my Mac so that one volume runs Mojave while the other runs Catalina.

I had already, I thought, set up a partition, optimistically entitling the new volume Mojave. But when I restart the computer holding down the Option key to dual boot, the screen only offers me a choice between my main volume and my external hard drive. The new Mojave volume does not appear.

I have downloaded Mojave Installer from the Apple Store but of course it won’t open because the Installer itself was created to run on High Sierra or earlier OS.

I at present use my external hard drive as a backup in conjunction with Time Machine. I could download the entire content from a date when I was running Mojave. This would presumably bring the Mojave OS with it. But, as explained, I can’t do this from inside the Mojave volume because I can’t get into the Mojave volume in the first place. If I were to download from inside the main volume, Catalina would be replaced by Mojave and all of the work I’ve done in the last few months would be obliterated. 

I suppose I could buy another external hard drive so that I’d have one for backup and one for Mojave. A solution perhaps, but an expensive one.

Any suggestions?