A (round-robin) tournament consists of n teams playing all possible matches. A Tournament Rule takes as input the results of a tournament and (possibly randomly) selects a ranking of teams, with a prize associated to each place in the ranking. Two teams may manipulate their match outcomes to try and improve their total expected prize winnings. Previous authors seek to understand the minimum manipulability among all "reasonable'' tournament rules (i.e. tournament rules so that if some team defeats every other team, it is ranked first with probability 1), when these two teams fix the match between them. Our work instead considers the possibility that two teams may both fix the match between them, and additionally throw matches to outside teams (that is, they can intentionally lose a match to a non-colluding team that they could have won). This model is more representative of the broader set of incentives at play and better captures real-world occurrences. Our main result establishes that no two teams can gain more than 1/3 of the top prize in expected prize winnings in the "Nested Randomized King of the Hill" tournament rule, by together fixing their match and throwing matches to external teams. This is optimal, as any "reasonable'' tournament admits the possibility of two teams gaining 1/3 in expected prize-winnings just by fixing the match between them.