Can I mention multiple faculty members in my SOP? 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.
I'm in a program (and went to a program) where students are admitted to the program, not a lab.

When considering students, I'm actually quite nervous about those who only mention a single professor they're interested in working with, as that's not a particularly robust "plan". What if they don't get tenure, or are recruited elsewhere? What if they have a personal emergency? What if they just don't have funding for a student right now? What if it turns out you just have wildly incompatible working habits (this happened to me)?

I'm going to echo Buffy's suggestion - don't try to write your SOP as the optimal solution to a game whose rules you don't know. Write about your interests in the program, and how that applies to one or more specific faculty members.