REST API Url Query

This is a hypothetical situation to illustrate the problem. I realize that this could likely be solved another way.

There are 3 SharePoint Lists:
PersonList -
--Name
-- AddressLookupColumn
AddressList-
-- Address
-- AddressTypeLookupColumn
AddressTypeList-
-- AddressTypeName

Using the OData spec I can do something like:

http://mysite/_api/web/getByTitle('PersonList')/items?$select=Name,AddressLookupColumn/Address&$expand=AddressLookupColumn

That will give me Name and Address. What I need is the Name, Address, and Address Type.

I think should be able to do:

http://mysite/_api/web/getByTitle('PersonList')/items?$select=Name,AddressLookupColumn/Address,AddressLookupColumn/AddressTypeLookupColumn/AddressTypeName&$expand=AddressLookupColumn,AddressLookupColumn/AddressTypeLookupColumn 

.. in order to get Name, Address, and AddressTypeName

Does SharePoint support that? If so, what am I doing wrong in my query?