Emulate OS 10 or OS 11 on Monterey 12.7.6 ?

Forget the emulator.

As alternative to using an emulator, have you simply considered installing the earlier macOS version(s) with your legacy apps on an external SSD and boot from that whenever you need to? It's a pretty simple setup.

Which macOS 10 version are you interested in?

10.14 Mojave and earlier can run old Mac software of the 32-bit variety.

10.15 Catalina and macOS 11 Big Sur cannot run 32-bit apps but requires all software to be 64-bit coded.

Angus McC wrote:

I don’t have the installation disks for the OS 10, sadly, so I don’t know how I’d install it on an external drive. Unless I misunderstand, an emulator would include the OS 10, up and running and ready for me to install compatible apps. 

You want UTM.

https://mac.getutm.app/

Then you want to search for a Github project called "utmconfigs".

Bigwaff wrote:

Angus McC wrote:

I don’t have the installation disks for the OS 10, sadly, so I don’t know how I’d install it on an external drive. Unless I misunderstand, an emulator would include the OS 10, up and running and ready for me to install compatible apps. 

You want UTM.

https://mac.getutm.app/

Then you want to search for a Github project called "utmconfigs".

Disregard. I didn't realize they had it working for both systems.

Angus McC wrote:

Thanks for your thoughts, D.I.

The apps I’m most interested in running are my Adobe CS3 Suite (Illustrator, Photoshop, Acrobat). So any version of Mac OS 10 or OS 11 should do the job. 

How much memory do these apps require? Using any type of Virtual Machine on your Mac will require a minimum of 8GB for macOS itself on the host plus assigning at least another 8GB for the VM itself. A host system with 16GB of memory is barely able to facilitate such a setup. This is why using an external boot drive for the older OS is best.

While the idea of being able to boot the MacBook into those OS from an external drive makes great sense, two problems:

1. Ideally, I’d like to have both the OS 10.x, say, and the MacBook’s native OS 12.7.7 running simultaneously, so I can exchange data and files between apps on each system in real time, rather than having to save, shut down one OS, then boot up again in the other OS. Hence the appeal of an emulator, where, I imagine, the older OS would appear as a Window in the newer OS.

Understandable. I don't recommend dual booting for those exact reasons. However, 16GB of memory (assuming your laptop even has 16GB of memory) is borderline able to handle a Virtual Machine.

You would be better served by getting a newer Mac to use for every day while keeping this 2015 laptop to run your older software using an older OS (erasing the Monterey OS & installing an older version of macOS compatible with your software).

One problem you may run into is not being able to reinstall & activate the older Adobe software. Many major software vendors tend to turn off their software activation servers, forcing users to upgrade to newer subscription models which also require later versions of macOS. You may want to confirm whether you can even reinstall & activate your older Adobe software as this whole discussion may be moot.

2. I don’t have the installation disks for the OS 10, sadly, so I don’t know how I’d install it on an external drive. Unless I misunderstand, an emulator would include the OS 10, up and running and ready for me to install compatible apps. 

You can create a bootable macOS USB installer using the instructions in the following Apple article:

Create a bootable installer for macOS - Apple Support

No, having an OS on an external drive won't provide for the simultaneous use of two macOS versions.

To do that you might consider using VM Ware's Fusion virtual environment or something similar, maybe Parallels.

I'm pretty sure, however, that you're going to have to provide an installer for whatever OS it is that you're going to want to install. Apple provides access to installers and has guidance for downloading them here: How to download and install macOS - Apple Support

Of course, these installers may also be used to install macOS on an external drive IF the Mac is qualified to run them. Your mid-2015 MBP can run OS X 10.10 Yosemite to macOS 12 Monterey natively.

I suggest you determine the newest macOS that your old Adobe apps can run under (10.14 Mojave?) and concentrate on using that, whether via VM Ware (I wouldn't) or installed as a boot OS on an external drive.

To be honest, it's probably time to either find newer versions of those Adobe apps that can run in a newer macOS... or find replacements for them. To keep running the old apps will become increasingly difficult as hardware continues to age and fail.

A MacBook Pro (Retina, 15-inch, Mid 2015) would have shipped with one of

• OS X 10.10.3 (Yosemite), OS X 10.11 (El Capitain), OS 10.11.1 (El Capitan), or OS X 10.11.2 (El Capitain)

So you should be able to run the latest versions of El Capitan, Sierra, High Sierra, or Mojave dual-boot or in a virtual machine, provided that Monterey will let you run the installers.

How to download and install macOS - Apple Support

However, there is another obstacle. You say that you want to do this so that you can keep using your old one-time-purchase versions of Adobe software. Adobe may have shut off the DRM activation servers for your software. In that case, you could set up a dual-boot or virtual machine environment, and still not be able to use your old Adobe programs.

Note: When you say that "any version of OS 11 will do the job" of running CS3, I believe that you are mistaken. 11 is Big Sur and will not run 32-bit software. (El Capitan is 10.11.*)