Thanks for the reply! I thought putting 'new' in quotes would transmit the idea it isn't literally new. Wishful thinking on my part. It's a refurb. I asked that it come loaded with High Sierra, because legacy software. They said they would downgrade it for me, but when it arrived ... Catalina. I thought it would be faster to downgrade it myself, rather than send it back. Hoping someone could point me to the hiding place of the "previous version Installer".
I'm naive enough, I guess, to believe Apple would certainly have a version of the installer that could install, at least, the most recent previous version. Why wouldn't they? Compost happens. Someone discovers their new Mac won't run what, for them, is a critical piece of software. Or, worse yet, the new OS is buggy like crazy. So, give them an uncomplicated escape hatch. It's what I'd do if it was my company. Right?? Har! Shades of the rollout of Microsoft Vista. Given reported Catalina bugginess, I'm surprised someone isn't in the business of selling thumb drives with Mohave downgrade installers loaded.
I created a boot loader and got it running yesterday. Fortunately, I didn't need to be in a huge hurry.