Actually, it is possible! It just requires a little detour. Create the first drop
shadow as you normally would. Then right-click on the layer and select
“Convert to Smart Object” from the menu. This smart object can be
assigned another drop shadow, and you can convert the smart object into
yet another smart object. This way, you can easily add a third and fourth
drop shadow. Alternatively, you could apply multiple strokes.
Three shadows in combination.
By the way, to put one or even several styles onto their own layers at once,
right-click on the FX symbol and select “Create Layer” from the list. Now
you can apply filters to these styles, but they won’t be editable anymore.