When 3-season backpacking, time spent in camp usually involves, sleeping and eating without a big emphasis on "communal camp time". Further, most of the meals I take on a backpacking trip tend to require simple preparation. As such, I really would not find much value bringing a second tarp on a backpacking trip.
If the trip revolves around a 'base camp", a tarp, chairs and such might find their way into a packing list.
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