I would not worry about "flat" lighting as opposed to simply lighting the entire group evenly, metering edge to edge. This does not sound like a type of portrait where you have dozens of lights on set to create dramatic lighting. The difficulty with "feathering" light with a large group is where the shadows fall. If the faces are close together in the group, you need to watch how shadows will cut across the next subject. If you can, a single large (or two large umbrellas close together will become a large source) light source placed well above camera axis is the easiest way to light a moderately large group without worry about cross shadows. 32 is manageable. As the group grows in size, obviously might need to widen the throw/sources but take care to knock shadows down off faces.
Ken
This photo dates back to about 1924. The father is John F. Pimentel. He immigrated to America from the Azores through Ellis Island in the first decade of 20th century. His family moved to Fall River, Massachusetts, because the city had a large community of Portuguese immigrants
Bill Barbosa Photography. This photo was recently posted by the son of older boy on the left on the Fall River Facebook page. My wife and I are both from Fall River and the little boy in the middle is my father-in-law. He would have around 100-years-old in 2020.