Can a late 2013 iMac run an OS higher than Catalina?

No.

(262968)

claus237 wrote:

LINUX IS AN OPTION?

Yes, Linux OS is an option for that old iMac.

This is a nice version: Home - Linux Mint.

12+ years is a pretty good run for a computer. It might be time to start considering a replacement.

If you plan to continue using that iMac for a while, I would suggest grabbing a copy of Firefox . Catalina stopped getting the latest versions of Safari some time ago – and the current versions of many other Web browsers now require Big Sur or Monterey.

The current version of Firefox (148.0) will run on Catalina.

macOS 11 Big Sur is compatible with these computers

And the hardware requirement for every succeeding OS moves farther from your 2013 iMac.

LINUX IS AN OPTION?

yes, I know D.I Johnson.

I running LINUX MINT on a 2013 IMac.

Thanks, for your feedback!