I have a late 2013 iMac. Is there any way to run macOS Monterey on it? the last update OS was in 2018--High Sierra

As mentioned you can still upgrade to Catalina. If you are having difficulty using Software Update to do that, please navigate to:

How to get old versions of macOS

Read carefully and follow the instructions to upgrade to Catalina.

You cannot upgrade to Monterey but you can update to Catalina, and I reccommend doing so. Catalina still receives security updates while High Sierra doesn't

That model can't be upgraded past Catalina.

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