Can someone on a Non-O visa based on marriage to a foreigner obtain a work permit in Thailand?

Nope, that's the notable difference between those two non-O subcategories. So he will have to go abroad and get a non-B, or switch to it in-country if the employer can qualify for that.

He cannot 😕 ,

The Non-O visa/extension based on being married to a foreigner who legally works here cannot get a work permit or be employed. It's a "trailing spouse" visa with employment prohibited

They'd have to cancel the extension they're on, and then either bounce out/back to get on a free stamp entry where they could apply in country for the 90 day Non-B (If their employer can meet those requirements)

OR

they'd cancel the extension they're on, exit the country, go to a thai consulate nearby and get the 90 day single entry Non-B visa