iTunes/Mp3-Player and actual multi-tagging of MP3s
For a thorough analyse of the topic, read Ways to store multiple genres in your digital music, where Dan says:


  MP3. MP3s (or rather, the ID3 tagging format used by MP3s) don't support multiple tags for genre. Instead you must useone existing tag and use a delimiter character to separate the genres within that tag. 


If you use iTunes player, I'd recommend to use the Grouping tag for that purpose.  

Now, can you do that automatically ?
As you pointed out, Last.fm offers an interface to retrieve tags for songs.
And bdefore used that API to develop an iTunes Multi-Genre Tagger (description blog post here, last version of the script here). I think that's the tool you're after.