I have first-hand experience of this, and will share it here, for what it is worth.
Early this year I received a Non-O visa issued at Nonthaburi immigration. I was staying at an address in that province. Before I was able to apply for the first extension of stay, I moved to an address in Bangkok, and registered that residence with a TM30 at Bangkok immigration. Once I was within the last 30 days validity of the visa I applied at BKK for an extension, but was rejected as they were refusing to extend a visa not originally issued there. They told me to return to Nonthaburi and extend it there, but my application there was also rejected also as I had no longer lived in that province.
The rule seems to be that the first extension must be applied for at the office which issued the visa, and the applicant must still reside there. I have sought advice from some of the officers at BKK on how this will affect subsequent applications for extension, but have received conflicting answers, and my situation is still unclear. My advice is to stay in one place at least until the first extension has been granted.