The high-energy behaviour of scattering amplitudes involving massive particles has attracted interest in recent years. In these proceedings, we report on the analytic tool AsyInt for solving massive multi-loop Feynman integrals in the high-energy limit, which are fundamental building blocks for such amplitudes in the full Standard Model. We present recent analytic results for two-loop four-point Feynman integrals with both internal and external masses in this limit, featuring polylogarithmic and elliptic structures.