I'm having an old MacBook Air 4.2, (mid 2011, SSD, 4 Gb memory), which have been running Catalina for quite some time despite that the max OS is High Sierra. I have been using the great work by dosedudes1 and his Catalina patcher.
Unfortunately he didn't continue with patches for newer OS:s, but have helped with a new patcher. This patcher even handles Macs with graphic cards from 2008 - 2011.
Mac Os Catalina
If you have a Mac running on macOS Catalina, then there are high chances that your computer might not support macOS Big Sur officially. However, there are ways to install macOS Big Sur at least on some of the unsupported Macs like the mid-2012 or the early-2013 MacBook Pro. Mac Pro 2013 and later. MacBook Pro and Air Late 2013 and later. IMac 2014 and later. Mac mini 2014 and later. MacBook 2015 and later. IMac Pro 2017 and all later models.
Using the patcher i got the mentioned Mac up and running with Big Sur after just over an hour.
Fantastic !!!
Patcher manual
The manual for the OpenCore Legacy Patcher is nice and there are also a video that will help you for the whole process.
Create bootable USB
You start with creating a bootable USB with info from this post. Just pick Big Sur instead of the mentioned High Sierra.
Building/installing the patcher
Big Sur Mac Os Update
After that follow these instructions,on how to install and use the OpenCore Legacy patcher.
Good luck !
Remarks
Mac Os Big Sur Requirements
- Erase/format the MAC HD/SSD before installation !! I really think that this does it more simple for the installer !!
- 'Mac OS Extended(journaled)' with an old non SSD HD
- With en SSD use 'APFS'
- The Mac rebooted several times during install.
- Don't remove the USB until at the very end.
- If you, like me, have a Mac which need the legacy video acceleration support please note that the Mac have a painfully slow display update before you have applied the 'Post-Install volume Patch'.
- Updating the Mac from Big Sur 11.4 to 11.5, made the messages.app stop working fixed in release 0.2.4
- Please note that 'Nightly Builds' are available but are for testing purposes only !!!