Can you apply for more than one PHD at a time? And if so is there a max number you can apply for at one time?

Hey Ellie (I presume that's your name),

Indeed you can apply for multiple PhDs at the same time. In fact, if you are certain you want to do a PhD, it would probably be a bit silly not to, assuming there's a few you are interested in. Some application forms may ask about other unis/projects applied for. People on here sometimes ask whether it's best to say what else you're in for, or keep quiet. Personally, I think that, as long as the range of projects isn't huge, tell the truth - after all, if you're the best applicant, they won't reject you just because you've applied for other projects. They may, however, want somekind of assurance that, if you accept their place, you won't then take another. Whether this in enforcible is another question...

If you apply for one, and then leave others until you get a final decision, you may miss the boat on other projects you like the look of, so apply for what you want, and good luck!

I wouldn't recommend spreading yourself too thin. I waited for the right PhD to come up and then put my all my effort into getting it. I was also asked at interview if I had made any other applications.

Problem is, you're still not guaranteed to get that one, however much effort you put into the application/interview.
Best bet is certainly to apply for many, even at the same institution! At the very least, it shows that you're committed to doing a PhD (although if you apply for two at the same institution, it's best that they are pretty similar subjects).
Apply to everything you think is interesting, and will give you good skills - the more you apply to, the greater the chance of getting one.

Apply to as many as possible. End of!

as many as you have the time to fill in all the forms for!!!