With pronouns, postpositions cannot be written separately. They combine with them and take different forms.
For example, the forms of मैं, हम, वह, आप corresponding to 'के पास' are 'मेरे पास', 'हमारे पास', 'उसके पास', आपके पास respectively.
With parts of the body, both forms can be used. (You can report if हमारा एक मुँह है is not accepted).
It's because depending on how you think of it, you can consider them to be your physical/tangible possessions or those that are intrinsic.
why is it not the plural 'hain' [हैं] ?? given that WE have that mouth? I just need the grammatical rule... I can see that it's related somehow to there being only ONE mouth... but struggling to understand it all...