The use of Metal-Organic Frameworks as crystalline matrices for the synthesis of multiple component or multivariate solids by the combination of different linkers into a single material has emerged as a versatile route to tailor the properties of single-component phases or even access new functions. This approach is particularly relevant for Zr6-MOFs due to the synthetic flexibility of this inorganic node. However, the majority of materials are isolated as polycrystalline solids, which are not ideal to decipher the spatial arrangement of parent and exchanged linkers for the formation of homogeneous structures or heterogeneous domains across the solid. Here we use high-throughput methodologies to optimize the synthesis of single crystals of UiO-68 and UiO-68-TZDC, a photoactive analogue based on a tetrazine dicarboxylic derivative. The analysis of the single linker phases reveals the necessity of combining both linkers to produce multivariate frameworks that combine efficient light sensitization, chemical stability, and porosity, all relevant to photocatalysis. We use solvent-assisted linker exchange reactions to produce a family of UiO-68-TZDC% binary frameworks, which respect the integrity and morphology of the original crystals. Our results suggest that the concentration of TZDC in solution and the reaction time control the distribution of this linker in the sibling crystals for a uniform mixture or the formation of core-shell domains. We also demonstrate how the possibility of generating an asymmetric distribution of both linkers has a negligible effect on the electronic structure and optical band gap of the solids but controls their performance for drastic changes in the photocatalytic activity toward proton or methyl viologen reduction.