We present a novel approach to the generation of new crystalline phases, which is based on a combination of the topological description of crystal structures as a periodic net and the extended Zintl-Klemm concept, which establishes the structural relations between chemically and structurally simpler and more complex inorganic compounds. With this approach, we have explored the structural similarities between all known binary sulfides, selenides, and the corresponding simple sulfates and selenates and have theoretically revealed seven new high-pressure phases in the last two groups of compounds. Using density functional theory methods, we have studied the thermodynamic and mechanical stability of the new phases, have adjusted the transition pathways in the sulfate and selenate systems, and have revealed new structural correlations of the baric polymorphism in these systems. The advantages of the topological approach compared to conventional methods of modeling crystal structures are discussed and illustrated.