We study mean curvature flows (MCFs) coming out of cones. As cones are singular at the origin, the evolution is generally not unique. A special case of such flows is known as the self-expanders. We will construct many non-self-similar MCFs coming out of a given cone provided there are more than one (smooth) self-expanders asymptotic to the cone. We then discuss a classification problem of such flows. In particular, we show that, in low dimensions, and when the cones are not too complex, the above solutions are all one gets.
