What are the URL Alias pattern replacements for taxonomy parent terms when building up Node paths?
There are some advanced uses of tokens (not sure off the top of my head if that's just in the context of pathauto or not). You can get what you're looking for with join:

[node:field-name:parents:join:/]/[node:field-name:name]/[node:title]


You could also replace your term pattern with:

[term:parents:join:/]/[term:name]


Using that method your vocabulary can grow gracefully to 4 (or more) levels without having to change the pathauto pattern.

You'll need to go to admin/config/search/path/settings and set the Slash (/) option to "Do not Replace" under "Punctuation" for that method to work.