I have a 15in 2017 MacBook Pro running High Sierra.. Can I update the software to Catalina or Mojave?

It can be upgraded to Monterey (the most current version) or to earlier versions.

See: How to upgrade to macOS Monterey - Apple Support

or

How to get old versions of macOS - Apple Support

Remember that older apps like Office 2011 (and older) will run on Mojave but not on Catalina.

This free tool may help you find which older apps would be affected if you do Catalina and if updates are available:

https://www.stclairsoft.com/Go64/index.html

There are no free upgrades from Office 2011 to a higher compatible version (Office 2021 or Office 365). IT must be repurchased

Yes. Back up your data, check your applications for compatibility, and click on Mojave or Catalina.

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Note too, that if you go all the way to Catalina or beyond, iPhoto won't work, either.