Like many intensional logics, William Parry’s logic of analytic implication $\mathsf{PAI}$ admits extensions determined by imposing semantic conditions on its account of modality. $\mathsf{PAI}$ is unique, however, in its allowing a second dimension—a topic-theoretic dimension—along which extensions can be defined. The recent introduction by Francesco Berto of topic-sensitive intentional modals (TSIMs)—which disagree with $\mathsf{PAI}$ on this type of condition—provide further motivations to examine such topic-theoretic extensions. In this paper, we introduce, motivate, and characterize a number of such extensions of $\mathsf{PAI}$, paying special attention to applications to Berto’s framework and to ways in which the modal and topic-theoretic dimensions influence one another.