iMac 2011 21,5" and the plan to install Mojave/Calatina using egpu  

@zywiec According to https://support.apple.com/en-gb/HT201634 , your iMac is the iMac12,1

According to the following pages, it is possible to upgrade to Mojave or Catalina, but it might not be a good idea because of the GPU in the iMac.
http://dosdude1.com/mojave/
https://forums.macrumors.com/threads/macos-10-14-mojave-on-unsupported-macs-thread.2121473/
http://dosdude1.com/catalina/
https://forums.macrumors.com/threads/macos-10-15-catalina-on-unsupported-macs.2183772/

You might be able to replace the AMD Radeon 6xxx in the iMac with a different MXM card.
https://forums.macrumors.com/threads/2011-imac-graphics-card-upgrade.1596614/

What might be cool is a MXM to PCIe adapter instead of using a Thunderbolt eGPU. I don't think it exists and you would probably need to cut a hole in the iMac to connect it. It's unclear if it would allow the internal display to work.
http://www.sourninja.com/dualwield/

@joevt Thank you for this information. Let's drop the idea with MMX to PCIe adapter. The project you mentioned was a kickstarter.  

MXM replacement will bring a lot of problems I guess. I had read the forum thread you put and this a long story. I am afraid I break my iMac. 

Summarizing. It is not possible to use a setup? iMac 12,1 updated to Mojave and then eGPU via TB1?

@zywiec

Read the dosdude1 guides. Read the first posts of the Mac Rumors threads. They suggest to disable the AMD dGPU by following the instructions at http://dosdude1.com/gpudisable/

Once you have Mojave or Catalina installed, you can try the steps to enable eGPU from Thunderbolt 1.

@joevt

iMac with discrete GPU does not have mux (and hence “no iGPU” even if hardware is present) so your recommendation will not work. The dosdude link is for MacBook pros only (that have dual GPU and mux) and it is the same technique I have been using in purge-nvda.

@zywiec

I suggest sticking to High Sierra with community eGPU support. Dosdude support alongside eGPU patches (even if you got Mojave/Catalina working) was also discussed here: https://github.com/mayankk2308/purge-wrangler/issues/28

@mac_editor

Right. I missed the part where it says "You CANNOT disable the AMD GPU in an iMac". So I guess you need to stick with High Sierra until an MXM option appears (which may be never).

I saw this video for working with the MXM card. Extreme:

Rominator was looking at MXM Mac rom for some nvidia card but didn't finished it:
http://forum.netkas.org/index.php/topic,13815.60.html