Commerce does not currently support this out of the box (March 2016) - but (just spitballing here, you'll have to try it all out for yourself of course) - you can add arbitrary custom fields to orders.
So you could rig something up by using e.g. a matrix of address field types like this one - https://github.com/elivz/VzAddress-Craft - to store the delivery addresses. But I am guessing you'd want the address data per line Item, so you could instead perhaps use the line items options system described at the bottom here:
...to add data for the address to each lineitem.
The order itself would have the purchaser's main address associated with it, but you could definitely store addresses either as options with lineitems, or in custom fields on the order, so it would be possible with some effort I'd say.
Also, you'd need to write a custom shipping solution or adjuster plugin that was capable of using the address data stored to calculate the shipping for each of the 'sub orders' and return the total, I suppose.
It's not going to be super simple but Commerce is very flexible and easy to work with when it comes to plugins etc.