How can I run multiple Skype accounts in one computer?

Run your first instance as usual, by clicking the icon.

Run the second one from terminal;

sudo /Applications/Skype.app/Contents/MacOS/Skype /secondary

I found the answer on this page. The command line arguments still exist, they have just been changed. Copying the format from this answer, we have the following command:

open -na /Applications/Skype.app --args --secondary --datapath="/Users/$(whoami)/Library/Application\ Support/Skype2"

Replace "Skype2" with as many numbers as you need instances of skype and go nuts.