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Other software is asking for OS X 10.11 or higher. But that OS is not offered on the software update. How can an Update the OS?
(Also, why doesn't Apple provide direct support for their products?)
iMac Line (2012 and Later)
The model year of an iMac is available at Apple menu > About This Mac.
An early 2009 iMac can be upgraded to El Capitan 10.11.6 but no later version. See: https://support.apple.com/en-us/HT211683
A late 2009 through mid 2011 iMac can be upgraded to High Sierra 10.13.6 but no later version. See: https://support.apple.com/en-us/HT211683
A late 2012 through late 2013 iMac can be upgraded to Catalina 10.15.7 but no later. See: https://support.apple.com/en-us/HT211683
A mid 2014 and late 2014 can be upgraded to the latest version of Big Sur macOS 11 but no later. See: https://support.apple.com/en-us/HT211683
A late 2015 or later can be upgraded to the current version of Monterey macOS 12. See: https://support.apple.com/en-us/HT212735
Also, Apple does offer support; there is a Get Support link at the top right of this page. Other alternatives are: Contact - Official Apple Support and Contact Apple for support and service - Apple Support
The model year of an iMac is available at Apple menu > About This Mac.
An early 2009 iMac can be upgraded to El Capitan 10.11.6 but no later version. See: https://support.apple.com/en-us/HT211683
A late 2009 through mid 2011 iMac can be upgraded to High Sierra 10.13.6 but no later version. See: https://support.apple.com/en-us/HT211683
A late 2012 through late 2013 iMac can be upgraded to Catalina 10.15.7 but no later. See: https://support.apple.com/en-us/HT211683
A mid 2014 and late 2014 can be upgraded to the latest version of Big Sur macOS 11 but no later. See: https://support.apple.com/en-us/HT211683
A late 2015 or later can be upgraded to the current version of Monterey macOS 12. See: https://support.apple.com/en-us/HT212735
Also, Apple does offer support; there is a Get Support link at the top right of this page. Other alternatives are: Contact - Official Apple Support and Contact Apple for support and service - Apple Support
The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.
With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install. For Best results use Safari to commence the download as Others may not work.
Safari will open a redirect and open the Apple Store where the download can commence
Tips Big Sir Upgrade Released Nov 2020
Tips Monterey Upgrade Released Oct 25, 2021
Make Time Machine Backup is very useful and can be used to Revert to Previous Working macOS
Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina, Big Sur & Monterey supports only 64 bit and there is no workaround.
Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.
Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal operation of the OS and may even Corrupt the OS requiring a Reinstallation
Other software is asking for OS X 10.11 or higher. But that OS is not offered on the software update. How can an Update the OS?
