Is it OK to send the same research proposal to several professors? I am a prospective PhD student in the humanities and I have already got in touch with a potential advisor in the university I would really like to work in. I have drafted a research proposal (as I have to submit one with my application) and sent it to him for feedback. 

At the same time, I am planning to apply at other universities as well, my first choice being very competitive. I have already found a couple faculty in other uni's I'd be also happy to work with (same research interests etc). Problem is they both require a research project draft when making first contact. 

My question is: is it OK or 'ethical' to send the very same research proposal to a few different potential advisors? How common is it? Am I really free to contact as many advisors as I want, hear from them and then pick the one I want to work with (assuming more than one are willing to take me in, on their part)? 

I know this might sound anxious but I really don't know how it works when it comes to the 'application etiquette.' Thank you all!
If you wrote the proposal entirely yourself, I see no problems with trying multiple universities. Do note the deadlines: you don't want to be in the situation that you need to choose between accepting an offer of a "lower-tier" university while still waiting for your first choice university to respond.
If you incorporate the suggestions of the faculty member of one university in your proposal to other universities, I'd at least let that faculty member know. Something like: "your university is my first choice, but as you know it is very competitive. Do you mind if I use this proposal to apply to other universities as a fallback"? This achieves 2 things: first of all it prevents a possible faculty member that might feel taken advantage of by using his/her comments to get into a different university. Second of all the advice you get might predominantly apply to his/her university, and might not generalize to other universities.