Is there an alternative way to upgrade my iMac 27-inch, Late 2013 from Catalina?

Sorry, a late 2013 iMac cannot be upgraded beyond Catalina.

Also see the following from Identify your iMac model - Apple Support

iMac (27-inch, Late 2013)

Model Identifier: iMac14,2

Part Number: ME086xx/A, ME088xx/A

Newest compatible operating system: macOS Catalina

Nothing interesting to be found. Apple simply does not support or provide any means to upgrade a Late-2013 iMac beyond macOS Catalina. Any approach at circumvention will not be supported in these communities and very likely will be removed by the Apple community administration team.

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I am having the same issue with my imac. Its like brand new even though its late 2013. If you find out anything sure would be interested

thanks so much. I suppose 3 inches doesn't make a big difference as long as it operates the same ports etc.

so its considered Junk? someone sent me a virus and glitched the system to Boot Loop...now its dead except the MAC Beep every 5 seconds after switching on....