TLDR: what's the smoothest way of getting a professor as a third advisor in the penultimate year of my PhD without offending my current advisors?
(Note: I know I am lucky and this is not a big problem, I just want to know the best way to proceed.)
I'm a penultimate year PhD working in field A in a top US university of that field. Since my masters, I've had two advisors that work in fields A&B. The relationship is great, they leave me great flexibility and they don't seem to care nor need recognition. My research started being close to another professor who was interested in my research. Last year I started meeting this professor weekly, separately from my weekly meetings with my regular advisors, and going to his lab meetings (and I told my advisors and they were fine with it). I've also now co-authored a paper with all three professors in it.
This Fall I will be on the job market. My current advisors are extremely well-known in field B, and one of them is also well-known in my field A, but this third professor is just extremely popular in field A. He also has a very good history of having students going to top places after graduation. Finally, our research interests align very well and his insights have been very helpful. I think it would be beneficial for me (and possibly for the third professor) to have him as an adivosr. I also know this is possible since a friend of mine has this same triplet of professors as advisors.
I really like my PIs and don't want to offend them. Is it offensive/unfair to my current PIs if I try to get this third professor as an advisor so late in my PhD (without dropping either of them)? If so, who should I ask first? And, is it better to do it via email to give them freedom to think about it or in one of my face-to-face meetings?
