したためる seems to be a formal word for finishing writing something of objective importance. But there is a second listing "to have (lunch, dinner), to eat" which I haven't found usages of. Is it used, and if so how does it differ from 召し上がる?
It is about the same politeness level as 食事を召し上がる, but it's a more literary way of saying it (It mentions it used in novels and plays to give a beautiful image)
