Extreme magnifications of distant objects by factors of several thousand have recently become a reality. Small, very luminous compact objects, such as supernovae (SNe), giant stars at z = 1 − 2, Pop III stars at z > 7, and even gravitational waves (GWs) from merging binary black holes near caustics of gravitational lenses can be magnified many thousands or even tens of thousands of times thanks to their small size. We explore the probability of such extreme magnifications in a cosmological context and include the effect of microlenses near critical curves. We show how the presence of microlenses near the critical curve sets a limit on the maximum magnification. We use a combination of state of the art halo mass functions, high-resolution analytical models for the density profiles, and inverse ray tracing to estimate the probability of magnification near caustics. We estimate the rate of highly magnified events in the case of SNe, GWs, and very luminous stars including Pop III stars. Our findings reveal that future observations will increase the number of events at extreme magnifications, and will open the door not only to studying individual sources at cosmic distances, but also to constraining compact dark matter candidates.