Our new, structurally consistent CASH+ sublattice solid solution model of calcium-silicate-hydrate (C-SH) has been successfully parameterized for the uptake of alkalis and aluminium. The model, developed by considering recent structural and atomistic views on C-S-H, can describe cation uptake, solubility, water content, and mean silicate chain length (MCL). End members for each cation have been defined by permutation of chemical moieties existing in two sublattices, and their properties along with the site interaction parameters were incrementally fitted against aqueous and solid phase composition and NMR-derived MCL data for a wide range of conditions (also considering incongruent phenomena). Good fits show that the model is incremental and can be extended stepwise (i.e. keeping previously fitted parameters fixed). Preliminary results show that the CASH+ model can be further extended for the uptake of iron, heavy metals, actinides, and fission products used in a broad range of cement chemistry and waste geochemistry applications.