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


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
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


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?
Additionally, is it disadvantageous to:

state in a PhD application that I am open to doing an MPhil?
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?
Typically departments (at least in the U.S.) will tell you on their website whether they have a preference about how you present your intentions.


I think you should try to get into a PhD program if possible.  However, you could apply to one or two master's programs just in case.

If your intention is to eventually get a PhD, just be honest about that.  In fact, for many departments, that would be a plus.


No one is going to hold you to what you write in your SOP.


They want to make sure you are motivated and have some sort of creative idea(s) -- but no one is going to check you against your SOP two years from now.

I'm not sure I covered everything.  To get useful responses, try to modularize.  It's okay to write more than one question.