Upgrading imac

Back up your data, check your applications for compatibility, and depending on which iMac model you have, click on El Capitan, High Sierra, Mojave, Catalina, Big Sur, or Monterey.

Catalina and newer won't run 32-bit software; download and use Go64 to scan for it. To check other programs, click here and look them up.

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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.

macOS Catalina 10.15 hardware requirements

macOS Mojave 10.14 hardware requirements

macOS High Sierra 10.13 hardware requirements

macOS Sierra 10.12 hardware requirements

OS X El Capitan - Technical Specifications

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

You need the link P Phillips gave you.How to get old versions of macOS - Apple Support If you scroll to the bottom half those are the downloads. Full installs. Click on the one you want and it will open up in the App Store. Check your computer, you may be able to go newer than El Capitan,

Think hard on upgrading. I just went from El Capitan to Monterey and I really, really hate Monterey. It is flat and gray. The font is so thin and small that my eye strain is horrendous. I am abandoning Safari -- I have actually downloaded Edge! I have tried adjusting the contrast, using color tints. I've spent hours trying to make things visible. It's killing me.

You are welcome and thank you too.

Do come back to the ASC Forums, ( Apple Support Communities ) in the future, if / or when additional question may arise

There are several points to consider before attempting the upgrade to Monterey.

The most important is Due Diligence on the part of the User and is a Prerequisite for a smooth upgrade.