I'm applying for PhD and thesis masters programs in Electrical and Computer Engineering. In one of the schools, there is a specific faculty member I'm extremely interested in working with. However, admission into her lab is really competitive. Realistically, my odds of getting in are mediocre at best.
At the same university, there is another faculty member who I share some interests with. I have also done research in his lab as an undergrad, and I know for a fact that he has millions in funding and more or less accepts any grad student who applies because he can afford to. He's definitely not ideal, but I'd be okay with doing my masters with him and then finding somewhere better for my PhD.
Finally, there's a third faculty member whose work is also pretty interesting. His research interests align fairly well with mine, but admission into his lab is also extremely competitive.
If I mention all three professors in my SOP, does it affect my chances of getting into the competitive labs? Obviously, if I only mention one name, it makes it look like I'm a lot more passionate about her work specifically. I was hoping for a way to maximize my chances of getting into the first prof's lab while still retaining the second and third prof as a back up. I was hoping for some advice on how I can phrase my SOP to accomplish this.