The use of di(2‐pyridyl)ketone in subcomponent self‐assembly is introduced. When combined with a flexible triamine and zinc bis(trifluoromethanesulfonyl)imide, this ketone formed a new Zn4L4 tetrahedron 1 bearing twelve uncoordinated pyridyl units around its metal‐ion vertices. The acid stability of 1 was found to be greater than that of the analogous tetrahedron 2 built from 2‐formylpyridine. Intriguingly, the peripheral presence of additional pyridine rings in 1 resulted in distinct guest binding behavior from that of 2, affecting guest scope as well as binding affinities. The different stabilities and guest affinities of capsules 1 and 2 enabled the design of systems whereby different cargoes could be moved between cages using acid and base as chemical stimuli. A strategy for improving the acid resistance of a tetrahedral cage has been developed by incorporating additional free pyridyl units on its vertices. The guest binding properties of the cage are also altered compared to the analogous tetrahedron without these peripheral groups, allowing the functions of complete cargo delivery and exchange between the two capsules by using acid and base as chemical stimuli.