| Hmmm, well there's the co-operative series of games. Battlestar Galactica and Shadows over Camelot both come to mind. Shadows is I understand the less complex of the two above. There's also pure co-operative games like Pandemic, Lord of the Rings and Arkham Horror. All high on interaction obviously since their co-operative games.
War games wise, for 4+ players, try Game of Thrones. Also, you might enjoy Risk 2210 or Dust. I'm not a huge fan of Risk 2210 but that's a personal taste thing, I know tons who love it. Note that most war games, especially for 4+ are going to be more complex than Agricola and Puerto Rico. No way around it. The closest that I know of to a simple 4+ one are the Risk 2210 and Dust games, or Memoir '44 with the Overlord expansion.
Last Night on Earth is really good, simple zombie game that is high on theme and since it's a 2-sided game, high on interaction inside parties.
And there's always the oldie... Diplomacy. All interaction. Though I prefer Intrigue (but that's a max 4 player game). | 
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