I use two computers for giving lessons. Some of my students use two devices, typically a phone for the video and audio, and a computer or tablet for reading articles.
I make (or receive) the call from my preferred computer (with webcam). On the second device, I select the same user for Skype chat. Now I can send text or documents to the person from either comptuer. Usually, I share the screen on the first computer and display an article to discuss or a corrected text. I can highlight sections of interest. On the second computer, I make discussion notes in the chatbox, and at an appropriate time, I pause the lesson to send the notes and then discuss them.