Recently, I ended up needing to run Skype using more than one account at the same time, so this is the way I found to riddle that out without using third party software of any kind.

1.- Open the Start Menu directory path and navigate to the Skype's folder. One quick way of achieving this can be pressing Win + R and typing the following:

%appdata%\Microsoft\Skype for Desktop

2.- Create a new directory there and call it whatever you want; I will call it TEST this time. After that, most likely you will have an existing Skype shortcut in your computer, so locate it, right click on it and press Open file location, then make a copy of it.

3.- Once you copy it, right click in the new shortcut and click on Properties. The only thing we need to modify is the Target field. By default it looks something like:

C:\Program Files (x86)\Microsoft\Skype for Desktop\Skype.exe

4.- So, to make it work as a secondary instance for Skype and allow us to run them both simultaneously, modify that path to this:

"C:\Program Files (x86)\Microsoft\Skype for Desktop\Skype.exe" --secondary --datapath "%appdata%\Microsoft\Skype for Desktop\TEST"

Don't forget to replace the --datapath option accordingly to yours.  

After this change, you can then double click the new shortcut and a new instance of Skype will pop up, allowing you to use both of them at the same time.