Third letter - begging

[Fleet23]

I'm in the awkward position of having run out of professors to ask for my third LOR. I did a 1-year master's program, and made pretty strong contacts with a couple of professors, but not with three apparently. Since I only took one class with most professors, and my thesis was overseen by a doctoral candidate, I just don't know whom else to ask. I've been rejected by three professors with whom I took one class, with good reason. They really don't know me well enough to write a strong letter. However, I received an A+ from one of these professors, and am considering replying to her rejection with almost a beg. I want to say that I know we didn't work closely together on any research, but that I am simply in need of a third recommendation which doesn't have to be as strong as the other two. I can provide my CV and explain how my interests align to my current work, but I still recognize that this letter may be weak. 

Would it be completely out of line to reply to a rejection in this way? Do I risk getting a torpedo of a rec?

[pro Augustis]

It seems like a risky tactic to me... Could you not ask someone from your undergard? 

[Elvidi]

If that is your only option, then I guess it's what you have to do - and if you play it right, it just might work (I would not, however, make it sound like that rec is basically a placeholder. the prof will probably not think it's worth their time). 

However, as stated above I'd lean more towards looking for alternative options ...

[Fleet23]

Thank you for your thoughts! Undergrad was 10 years ago, so I think they would have very little to say.

[Elvidi]

8 minutes ago, samsonite2pv said:

Thank you for your thoughts! Undergrad was 10 years ago, so I think they would have very little to say.

Would a professional rec be helpful to you at all? A current or recent supervisor?