Can Squarespace handle dropshipping?

I already have a webshop, but I'm considering to change system. At the moment an email is automatically sent to the right supplier when an order is received. Can Squarespace do something similar?

Not by default. But if you use the developer platform, you could integrate Shopify and use one of their many dropshipping add ons to make it work. Here is a previous post with some great information regarding Shopify + Squarespace integration (credit Jason Barone).

http://answers.squarespace.com/questions/4676/can-i-integrate-squarespace-commerce-with-shopify