You can't specify a depth (at least currently), but you could use this:
Go * EXPANDBRANCH=wild
That will expand all currently visible folders. It won't recursively expand them in a single click, but it'll expand another level each time you run it. So you could put it on a button or hotkey and click it a few times to open multiple levels.
(Could also have a script that runs it until there's nothing left to expand. Just make sure it doesn't loop forever if there's an error preventing expansion, e.g. due to folder permissions.)