Self-interacting dark matter (SIDM) provides an interesting alternative to collisionless dark matter, especially when it comes to resolving small-scale structure problems. I will present our (very) preliminary findings on gravothermal collapse in SIDM halos by incorporating velocity-dependent cross sections and going beyond the Born regime for the Yukawa potential. This allows us to explore a much broader range of parameter space and include significantly enhanced cross-sections in the non-born regime through resonances and other effects. We specifically investigate scenarios involving light mediators, which naturally produce velocity-dependent interactions and I will discuss the potential to establish new limits based on the expected stage of gravothermal collapse these halos are in.