Can I obtain a 60-day family visit extension once per entry, annually, or per visa in Thailand?

You're asking a question that is immigration office specific. 😕

The clause in the police order that allows 60 day visit thai family extensions doesn't spell out what "one time" means

Some offices interpret it as once per entry, meaning even on a multi-entry tourist visa or a year long, multi-entry visa (where you bounce out and back) you can get it once every time you enter the country

Some offices interpret it as once per visa, meaning you can get it one time on the visa you have and even if it's a multi entry visa once you take the 60 days you're done and can't get it again until you get a new visa

Almost ALL offices allow it one time on a yearly extension meaning if you have many years of extensions daisy chained together year after year IF you took the family extension during that time you're done and can't get it again.

Just had a guy denied the visit family extension on his yearly married to a thai extension because 2 years before when he was on his initial 90 day Non-O visa waiting to apply for the first year extension he'd used the 60 day extension. The office said, "same extension cannot" and he was denied the visit family extension

Didn't mean to make this answer so long, but the real answer is you need to go to your immigration office show them your passport and see if they'll let you get it or not. They have ultimate control over it