phd - MPhil applications - How flexible/sure should I be, and should I mention this possibility?

(I don't think there's a master of philosophy tag here)

I'm applying to PhD programs in pure math. I have a research master's degree in applied math. While it doesn't have a thesis, it has a course project. I've been reading about requirements for PhD programs and it turns out US-style PhDs expect only a bachelor's and a statement of purpose while European-style PhDs expect a (research) master's degree

I'm applying to universities places not in Europe or in the US that are somewhere in the middle. These universities offer MPhil.

Now, I have a feeling I won't be seen by universities as qualified for PhDs but will be qualified for MPhil. My ultimate goal is to pursue a PhD. I am perfectly fine with having to do an MPhil first.

My understanding is that

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  if I would apply for a PhD, then I should specify a certain area of math (for a statement of purpose; for a research proposal that's just the basics I guess) which I should be sure about researching otherwise I am a candidate who is not sure about research interests

  
  


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  but if I would apply for a master's, I should be flexible and thus state a certain area/s of research as merely a possible route

  
  
  
  
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     So what should I do for a statement of purpose for MPhil, which is somewhere in the middle of a master's and PhD? How sure/flexible should I be?

     
     
     
  
  
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     Additionally, is it disadvantageous to:

     
     
  
  
  
  


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  state in a PhD application that I am open to doing an MPhil?

  
  


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  apply for both an MPhil and a PhD in the same university?

  
  

I am concerned that doing either will count against me in being accepted for a PhD because it seems like I'm not so sure of myself.

I was advised to ask the admissions offices of the universities but that seems to me like asking a jury how to appeal to the same jury. I would ask a lawyer how I would appeal to the jury.

I was advised also to apply to MPhil's in some universities and PhD's in others. What do you think?