Does anyone know of a way (or if it's even possible)to add a 3rd interaction to a Hot Spot question?

Yes we can, there is an option to add more than 2 clicks in Interaction column.

https://community.qualtrics.com/XMcommunity/discussion/comment/40511#Comment_40511grahulp5 , how? I only see the 2 options (dislike/like; on/off). Please advice.

jbanaya When you select this question type, there would be some options available to add in left bar from where you select the question type. There you will find the required option.
Hope this helps!

grahulp5, this is the screenshot from the left bar. A third interaction type is not an option.

I think the issue here is that in mine login, I have some other options available too; I think it comes with other brands.