  In the present paper we describe compatible open books for the fibre
connected sum along binding components of open books, as well as for the fibre
connected sum along multi-sections of open books. As an application the first
description provides simple ways of constructing open books supporting all
tight contact structures on $T^3$, recovering a result by van Horn-Morris, as
well as an open book supporting the result of a Lutz twist along a binding
component of an open book, recovering a result by Ozbagci--Pamuk.
