In Photoshop we can have multiple dropped shadows be applied to a single object, and they all get layered upon each other. It gives users flexibility to use different colors, densities, feathering, etc.

In Illustrator, on the other hand, the Appearance works differently. Each new Drop Shadow get applied to the previous dropped shadow. The larger the blur is, the more useless the next shadow gets.

To get a layered shadow the same way we do it in Photoshop, we have to apply each shadow to its own fill.