There’s a reason it’s not officially supported…could be performance, could be something else entirely. However…I can definitely say that my 2014 mini which is updated to Monterey is too darned slow for anything but what it’s used for…which is a network destination for copying /Users on our laptops.
That’s great!! Screen sharing is a big part of my workflow. Thanks for the update 
Diane
What I mentioned before is true based on what Apple says and what most users do. I have looked at OpenCore previously but since a number of users were having issues and it does modify firmware if I recall correctly, it just wasn’t the safest thing to do. Since I only have so much time it wasn’t worth the bother as Catalina is fine for me. As I said before, I have Monterey running in a VM with VMware Fusion so if I really needed it for something I would use that if possible or just get a new Mini. I have done a Hackintosh many years ago and some of these patchers are similar to that process. I tried one of the dosdude ones to upgrade a 2011 Mini and nothing worked. So I suppose if one has the time to experiment then go for it but there is a reason why Apple doesn’t support some models with these newer systems and it usually is a graphics card/chip or a broadband card/chip in my experience.
As I stated in another post, I agree fully. Even if the processor is up to speed, there are too many other variables at play and by the time you figure it out, you realize you had better things to do.
Speaking of upgrading…I ordered a Studio and display 10 days or so back…the display was supposed to arrive 4/18-25 and the Studio itself next month 5/21-28. No matter though…the Studio shipped yesterday and will be here Monday according to UPS while the display is still shown as processing in the Apple store with delivery 4/18-25. Strange…but still better than the delivery dates for the Nikon Z9 and 800mm lens I ordered…I’ll be lucky to have them by July.
What I learned the hard way with my old 2010 Mini is that “too damned slow” to run a new Mac OS is dangerous if you are a fast touch typist using Mail. It misses keystrokes and deletes things that you don’t want to delete.
I have an old Core i5 Mac mini from late 2012 here and it’s still in good use at work for the occasional headless number crunch. IME an old Mac can absolutely still be used with more modern versions of macOS provided a) you install a SSD as a boot/scratch drive and b) you make sure it’s got enough RAM. I cannot fathom using any Mac these days booted off of or running work from a HDD. And particularly on Intel, I find anything below 16 GB RAM almost entirely unworkable.
I am curious about what you can do as “headless number crunch”.
FYI, my old Mac mini i7 spins up its fan when doing anything compute-intensive, so I don’t much of that.
Oh the fans sure spin up, but since this is in a work environment with a lot of other equipment with fans nobody would notice. The old Core i5 is still plenty fast to run some of our more simple simulations. These are single-threaded chunks of C code that usually complete within 48 hrs. We’ll often run many instances of the same code using different random seeds that generate perturbations to the system — that way we get an idea of what a typical experiment could return (you don’t know the exact perturbation ahead of the experiment, you only know what roughly the statistical distribution of expected errors is). So essentially what you need is a cheap system with a few cores available to run some of these jobs in parallel. You can either do this on a fancy new system with lots of cores, or you can simply recycle several older systems with idle cores. This old mini is good for running another 4 instances at a time. Since this is straight up C code that generates output files with absolutely no UI, all you need is a headless system with SSH access and gcc on it.
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Thanks for the information! 
[EDITED beginning to add official Apple download info.]
A tip for those of you buying older systems with the intention of running an older macOS version (ie. 10.12 Sierra through 10.15 Catalina).
You can download the full installers directly from Apple:
…
If this method does not work for you, you can download them from Apple with the help of dosdude1’s patchers. This method is a bit more complicated and is intended for those trying to install macOS on unsupported systems, so be careful.
While dosdude1 wrote these for a different purpose, it is still useful for getting the big installers if the Safari method does not work. Ignore all the technical info and warnings for each macOS version and just download the relevant tool. Then follow the steps below.
As an example, I just used dosdude1’s Mojave Patcher during a wipe and reinstall of my used 2014 mini i7 that shipped from OWC with Catalina because I needed 32-bit software support.
The trick with dosdude’s patchers is to stop before the install and locate the download option in the menus. Below is my procedure, although it may be slightly different depending on which dosdude1 patcher you use:
- Launch dosdude1 patcher
- Cancel/OK to get to main patcher window
- MENU: Tools > Download macOS [version]
- YES
- Choose save location
- Begin download
When finished, you can use the option to make a USB device with the macOS installer, or just follow the Apple procedure:
If the macOS you downloaded is NEWER than what you are currently running, simply drag the macOS installer into the Applications folder and run it.
As always, when the install is completed, be sure to scan for updates with Apple. Then reboot and run Howard Oakley’s Silent Knight to check for recent security updates to XProtect, MRT, Gatekeeper, TCC, etc.
If you will be using the older macOS online, at least run the current Firefox as default browser with strong security settings and install the add-on, uBlock Origin by Raymond Hill (beware of copycat versions). I also suggest the free Firewall tool, Lulu by Patrick Wardle as a simple alternative to Little Snitch and others. Lulu runs on macOS 10.15+ but scroll down a little and you will see a link to the older v1.2.3 which should run on macOS 10.12 - 10.14.
I would then BLOCK every app except Firefox from accessing the internet. Also only allow macOS processes that are essential to your needs. Block Safari and Help Viewer. I would even open Safari and disable everything you can including JavaScript and auto-fill, then clear all data in Safari and never open again.
There are many other tweaks but these are an excellent start if you are a good, defensive web surfer. 
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Did you just buy that Mini? My i7 was supposed to come with Monterey but it had Catalina. Not the biggest of deals as that’s what I needed for Turbotax, but if I want to use that next year I have to upgrade it.
I don’t like some of the Finder changes, like the dock springboard downloads file list, and having to do a drop down to change the Finder view (column, list).
Diane
The information you provided is great but for those less technically inclined, I think it might be easier just to download directly from Apple so as not to confuse any parts of the dosdude instructions:
Good point. Thank you. I just edited my post to add your link at the top with a warning. I should be careful when posting things late at night. 
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Ordered my i7 March 30th but it shipped the following week and came with Catalina. Just made a USB boot drive with the Mojave installer and started over.
Not sure what you mean exactly by “dock springboard downloads file list”?
Can you edit the Finder toolbar (right-click > Customize Toolbar)? On any new Mac setup I always make sure the Path, View and Action buttons are default.