Student or Learner
Does this "would" denote an opinion or suggestion(request) or presumption? Maybe presumption, but I'm not sure.
ex)My wife, Janice, and I have seen a marked decrease in our daughter, Noreen's, performance in your science class during the last two grade periods. We'd like to make an appoinment with you to discuss your ideas on what might be causing the problem...Mrs.Hamilton in the main office tells me that your regular conference period runs from 3:30 p.m to 4:30 p.m on Tuesdays, Wednesdays, and Thurdays. Would it be possible to meet with you next Wednesday, March 11, at 4pm? Please leave a message on our home answering machine confirming this day or suggesting an alternative. Because my wife's work regularly takes her out of town during the day, 4 p.m would be the earliest time we both could meet you. Our number is 968-9696. We'll wait to hear from you.
I think it's being used to be polite- it means that 4pm is the earliest, but using would sounds less direct, less demanding.