How To Add Multiple Drop Shadows In One Layer

The Smart Object workaround will work for you, but don't forget to uncheck 'Use Global Light' or when you change the light direction for the second and third drop shadows, you will also change, and mess up, the first one.

There are so many really cool, and highly useful changes with Photoshop CC, and getting more and more with every update.  Is $10 a month really too much to pay for all that power?  You'll still have CS6 to go back to if you decide you don't like it, but I'd better warn you that once you get used to all the extra features, you'll never want to have to do without them.

this can be done faster in the new Photoshop CC  where you can add up to 10 shadows on each Layer very easily.

your screenshot shows you are in the CS6 Version,

here is a workaround, Add shadow to One layer, convert it to smart object then add another shadow to the smart object layer

Layer-Layer Style-Create Layer, will put the drop shadow on its own layer. Then you can add another to the original.