IMac upgrade?

Even if you could do upgrade, it would require upgrading the entire system, i.e. buying a new computer.

macOS Mojave - Technical Specificationshttps://support.apple.com/kb/SP777?locale=en_US

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top

left of your screen and choose About This Mac. These Mac models are

compatible with macOS Mojave:

• iMac (Late 2012 or newer)
• iMac Pro (2017)

It is not possible to do a hardware upgrade for that system outside of RAM and SSD.

The mid 2011 iMac 21" officially tops out at 10.13.6

Its possible, but very difficult and very very unsupported.

On a scale of 1 to 5 where 1=trivial, 5=technician serviceable, 6=unsupported, and 10=truly_impossibly upgrading a 2011 iMac's GPU and installing Catalina is maybe an 8.

Madmen with mad skills have done it, but as far is this forum is concerned you are completely off the map.

No. It's gone as far as it can go.

Sorry, the 21.5 inch iMac is a closed system that cannot be easily upgraded.

No. In order to run Mac OS beyond 10.13.6 you must have a new Mac. Newer versions of Mac OS require Metal which is functionality of the GPU. iMacs made from 2012 on support Metal, iMacs made prior to 2012 cannot be upgraded. If you want to learn what Metal is please click https://developer.apple.com/metal/