Sending a second follow-up email for a potential PhD position Four weeks ago I contacted the department of the University to ask whether there are PhD positions open. They emailed me some questions I needed to fill in and said that they will review my application and let me know if they have something available for me as soon as possible. After two weeks, I sent a follow-up email asking if there was already some news about my application, but they didn't respond.
Now, two weeks after that follow-up email, I still haven't heard anything. Is it okay to send a second follow-up email? How should I formulate it? I don't want to seem annoying and intrusive. On the one hand, I'm willing to be patient as I really want to pursue a PhD at that faculty, but on the other hand, if they don't offer me a position, I need to start looking for other positions as soon as possible.
It's typical to apply for multiple (10+) PhD positions simultaneously, rather than sequentially. Don't wait to hear back from this place, just send your other applications now. It's fine to ask again about your application, but this time ask for the date by which you can expect to have a decision.
Here's a suggestion for how to formulate the email (you can modify it according to the specific details of your situation):

Dear Prof. X,
Last month I applied for a PhD position in your department. Do you
have any further news about my application, or an idea of when you
might make a decision? I am really excited about this opportunity and
look forward to hearing from you soon.
Best wishes,
MDG1999