” if the HMR read signed by three different communities all in Brooklyn”
It needs BOTH i.e. Kehilos and States, lets say Satmar in CA and NY sign it will not render as two.
Given the reason we need sep states is for the fear of one influential manipulating his communities Rav/Bet Din into one heter, (Note there is a machlokes regarding the very reason, see Meshav Davar of Netziv) the same applies to the Kehilos..