We treat the input-to-state stability (ISS) of linear continuous-time systems with multiple timescales. Such systems contain rapidly-varying, piecewise continuous and almost periodic coefficients with small parameters (time-scales). For systems with a single small parameter, a novel time-delay approach to averaging was recently introduced, whereas a complementary method for systems with multiple independent small parameters has been presented lately by the authors. The latter method relies on a novel system transformation, leading to a new system whose ISS guarantees the ISS of the original one. In this work, we unify this transformation with a new superposition-based system presentation. We employ timevarying Lyapunov functions for ISS analysis, where the novel system presentation plays a crucial role in deriving essentially less conservative compensating upper bounds. The analysis yields LMI conditions for ISS, leading to explicit bounds on the small parameters, decay rate and ISS gains. The LMIs are accompanied by suitable feasibility guarantees. Numerical examples demonstrate the efficacy of the proposed approach in comparison to existing methods.