The uniform interpolation results for modal logics like K, GL, and iSL can be extended to other modal logics or fragments by following a similar proof-theoretic approach. The key lies in defining the propositional quantifiers for the specific logic, ensuring correctness and termination of the proof search strategy, and proving the uniform interpolation property. By adapting the definitions and proof techniques to the specific axioms and rules of the target logic, one can establish uniform interpolation for a wide range of modal logics. This process may involve modifying the functions that compute the propositional quantifiers, adjusting the termination criteria, and proving the necessary implications and uniformity properties for the logic in question.