We have both a double and a triple.
I captain and take my kids on the rear.
We tend toward rural dirt roads, and it's hilly.
I have to be very conscious of how long the bicycle is as we take curves on our narrow rural roads.
It's possible to strike something on the inside of a curve or turn with the rear of the bike even though you have cleared it with room to spare up front.
So I am not sure it would be easy to go up to a quad......