Actually unless you're going to hack it, macOS 10.14.6 is the Highest OS it can run if you have a Metal-capable graphics card, if not then 10.13.6 is it.
macOS High Sierra - Technical Specifications
General Requirements
- OS X 10.8 or later
- 2GB of memory
- 14.3GB of available storage to perform upgrade*
- Some features require an Apple ID; terms apply.
- Some features require a compatible Internet service provider; fees may apply.
Mac Hardware Requirements
For details about your Mac model, click the Apple icon at the top left of your screen, choose About This Mac. These Mac models are compatible with macOS High Sierra:
- MacBook (Late 2009 or newer)
- MacBook Pro (Mid 2010 or newer)
- MacBook Air (Late 2010 or newer)
- Mac mini (Mid 2010 or newer)
- iMac (Late 2009 or newer)
- Mac Pro (Mid 2010 or newer)
macOS High Sierra - Technical Specifications - Apple Support
https://itunes.apple.com/app/macos-high-sierra/id1246284741?mt=12
macappstores://apps.apple.com/app/macos-high-sierra/id1246284741?mt=12
Thanks to Arty on getting full installer…
Looking for High Sierra installer - Apple Community
Terminal workaround for The Recovery Server Could Not Be Contacted Error!
https://www.youtube.com/watch?v=ouNQS36dIBw&t=95s
macOS Mojave 10.14.6 - Technical Specifications
General Requirements
OS X 10.8 or later
2GB of memory
12.5GB of available storage (OS X El Capitan 10.11.5 or later)*
Some features require an Apple ID; terms apply.
Some features require a compatible Internet service provider; fees may apply.
Mac Hardware Requirements
For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Mojave:
MacBook (Early 2015 or newer)
MacBook Air (Mid 2012 or newer)
MacBook Pro (Mid 2012 or newer)
Mac mini (Late 2012 or newer)
iMac (Late 2012 or newer)
iMac Pro (2017)
Mac Pro (Late 2013; Mid 2010 and Mid 2012 models with recommended Metal-capable graphics cards)
https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12
Thanks to MartinR Terminal command…
softwareupdate --fetch-full-installer --full-installer-version 10.14.6
It will place a copy of the installer in your Applications folder and you can use that to create a bootable installer.
MacOS Catalina 10.15.7 - Technical Specifications
General Requirements
OS X 10.9 or later
4GB of memory
12.5GB of available storage (OS X El Capitan 10.11.5 or later)*
Some features require an Apple ID; terms apply.
Some features require a compatible internet service provider; fees may apply.
Mac Hardware Requirements
For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Catalina:
MacBook (Early 2015 or newer)
MacBook Air (Mid 2012 or newer)
MacBook Pro (Mid 2012 or newer)
Mac mini (Late 2012 or newer)
iMac (Late 2012 or newer)
iMac Pro (2017)
Mac Pro (Late 2013 or newer)
How to download and install macOS - Apple Support
https://apps.apple.com/gb/app/macos-catalina/id1466841314?ls=1&mt=12
macappstores://apps.apple.com/app/macos-catalina/id1466841314?ls=1&mt=12
How to upgrade to macOS Catalina – Apple Support
And caution on 10.15 or higher, to see which Apps will no longer work in 10.15 get Go64...
https://www.stclairsoft.com/Go64/
