Back to the original question, I am actually likely to experience this scenario via a sizable inheritance my wife reasonably expects to receive in the next decade or two. While we have been conservative to have not factored this into our ER calculations, in the likely event that it happens it will potentially double to quadruple our current stache.
We are in the camp of our ER stache being already "enough", with contingency, for a planned burn rate that is very unlikely to change with any new found wealth. My thought at this stage is to establish a family trust that perpetually assists, rather than lump sum cashes up, my parents, children and siblings (in that order) over their collective life expectancies. In doing this, I am mindful of the Warren Buffet quote that goes: "I want to give my kids just enough so that they would feel that they could do anything, but not so much that they would feel like doing nothing." and apply that to my entire family unit.
That's the plan anyway, although I am yet to research how to set something like this up and indeed whether it is practically possible, especially beyond my own existence on this earth. I'll put this task on my ER to do list.