If your method involves you running multiple instances of the battle.net client (and therefore copied directories of the D2r game files eating up all of your drive space) then you are doing it wrong.
There's loads of guides on YouTube but unfortunately, they're almost entirely outdated and/or terrible.
To keep within the rules of this site, here's a method without using any other 3rd party apps*/scripts, you can launch the game by simply creating shortcuts on your desktop to your game (no battlenet client).
Note: *Exception to this is you will still need either procexp or handle64.exe to close the "Check for other instances" handle in the same ways that have been described elsewhere on this site and in other guides.
1. Browse to your Diablo 2 Resurrected game install folder (you only need one install folder).
2. Right click on d2r.exe and create shortcut. Copy shortcut to desktop.
3. Edit the shortcut and append the target field with:
Code
-username YourBnetEmail -password YourBnetPassword -address <REGION>
3a. * <REGION> could be us.actual.battle.net, EU.actual.battle.net or KR.actual.battle.net for Americas, Europe or Asia respectively.
4. Rename shortcut to your linking.
5. Copy shortcut and edit username and password for second account. Repeat for additional accounts.
6. Launch 1st instance of game from shortcut.
7. Kill handle as per your handle killing method.
8. Launch 2nd instance of game from shortcut.
9. Kill Handle this this subsequent instance
10. Repeat steps 8 and 9 for subsequent accounts.
You can either copy a shortcut for each account and region or simply keep one shortcut per account and edit address details the shortcut when you want to switch regions.
Drawback with this method is that Blizzard forgot to make this work with MFA, which is kind of moot anyway as Blizzard prevent you from using standard MFA apps that allow additional accounts.
If you have issues logging in, try logging in manually into battlenet as sometimes there are captcha codes (especially if you typo your email or password).