Apply for PhD positions with only one (or no) reference (letter of recommendation) After applying for a number of PhD positions I ended up with a surprisingly high rejection rate, and as little as 3 acceptances. Waiting for a positive answer from other labs (which I liked a lot better), I ended up inadvertently losing these 3 offers as well.

This seems to have been very unwise in hindsight, but at the time I did not believe I would get so many subsequent rejections (I still find it hard to believe...).

In any case, I have to apply to more labs now, and one of my referees refuses to provide further references for me because he already did it for quite a few of my applications, and is also - in his own words - "more than irritated" that I took the liberty to turn down any offers at all. I can't say I entirely disagree with him, since I actually did feel a bit guilty in the first place for asking him to be my referee for so many applications.

So, here I am, and I would be very curious whether you have any ideas:


If there is anything I could say to maybe change his mind (currently not responding to my emails).
If there is any way to make people whose labs I apply to understand why I can only provide one reference without completely ruining my chances. 


Sadly, I am applying for a field a bit different from what I nominally studied (cognitive neuroscience as opposed to molecular neuroscience), and there are no other referees I can choose from with whom I have worked on cognitive topics. Also, the referee in question was my MSc. supervisor, so I would immagine people will like to hear from him anyway.
The answers to your questions relatively:


No. He is currently very angry with you. Because probably he lost a lot of reputation. A letter of recommendation does not only mean "Take this guy, he's great.", but also means "I entirely trust this guy and I guarantee that he will not leave you in the lurch." By getting acceptance and not taking the offer is usually interpreted as hesitancy. Thus, people from the labs you've turned down will consider your advisor as someone who easily recommends a student. They will think that a student does this even at the beginning will easily give up on tough research duties.
Conspiracy theory: the subsequent rejections may be the result of grapevine. In my country, top universities' professors are usually classmates or former colleagues. If a student applies with a good background and strong recommendations, they call each other and ask about that student. You know, if that they ever heard about that guy, who is considerable. And guess what if one or two of them told: "I accepted him and he ended up not even starting."  


I think, for a short period of time, you should lower your standards. Try applying a lab in your field.

Don't send consecutive mails to your advisor. Talk to him face-to-face. Ask him if you can do something to make it up. At that point, you should be prepared to take no for an answer.