What paperwork is needed to extend a Non-O multi-entry visa in Thailand, and will it remain a multi-entry visa after the extension?

You have 3 choices

You apply for a 60 day visit thai family extension based on marriage to a thai

You apply for a yearly extension based on marriage to a thai

you do NOTHING and suck up the free amnesty and when the borders re-open you go get another year-long, multi-entry Non-O visa based on marriage from a thai consulate nearby.

I'd say GO for the year extension (seeing as there is NO proof of funds) for foreign women married to thai men when they get the yearly extension. THEN after you get the extension get a re-entry permit

I highly recommend getting a one year extension of stay based on being married to a Thai man. Unlike an extension of stay based on marriage to a Thai woman, there is *NO* proof of income or savings requirements.

Extensions of stays <- that you get from the immigration office inside thailand are sold as WITHOUT any re-entry <- that's because you're already INSIDE thailand. SO once you get the yearly extension you would BUY a re-entry permit, (either a single entry for 1000baht that lets you leave/come back once during the year or a multiple entry for 3800baht that lets you leave/come back as much as you want to for the year the extension is valid for)

Sadly there is NO one size fits all list of documents SO

you need to GO to the immigration office before you need your extension and get the hand out that lists the documentation requirements to get a yearly extension of stay based on being a foreign woman married to a thai man.