Post-translational modifications (PTMs) of proteins play a vital role in their function and stability. These modifications influence protein folding, signaling, protein-protein interactions, enzyme activity, binding affinity, aggregation, degradation, and much more. To date, over 400 types of PTMs have been described, representing chemical diversity well beyond the genetically encoded amino acids. Such modifications pose a challenge to the successful design of proteins, but also represent a major opportunity to diversify the protein engineering toolbox. To this end, we first trained artificial neural networks (ANNs) to predict eighteen of the most abundant PTMs, including protein glycosylation, phosphorylation, methylation, and deamidation. In a second step, these models were implemented inside the computational protein modeling suite Rosetta, which allows flexible combination with existing protocols to model the modified sites and understand their impact on protein stability as well as function. Lastly, we developed a new design protocol that either maximizes or minimizes the predicted probability of a particular site being modified. We find that this combination of ANN prediction and structure-based design can enable the modification of existing, as well as the introduction of novel, PTMs. The potential applications of our work include, but are not limited to, glycan masking of epitopes, strengthening protein-protein interactions through phosphorylation, as well as protecting proteins from deamidation liabilities. These applications are especially important for the design of new protein therapeutics where PTMs can drastically change the therapeutic properties of a protein. Our work adds novel tools to Rosetta's protein engineering toolbox that allow for the rational design of PTMs.