many_to_many detailed in DBIx::Class::Relationship is what you want, I think. FWIW, it sounds like your data is set-up well. Refactoring the tables for this would be a mistake. Fake, untested code for your case–

{
    package MyApp::Schema::Result::League;
    # ...
    __PACKAGE__->has_many( league_teams => "MyApp::Schema::Result::Lea
+gueTeam", "league" );
    __PACKAGE__->many_to_many( teams => "league_teams", "team" );
    # ...
}

{
    package MyApp::Schema::Result::Team;
    __PACKAGE__->has_many( league_teams => "MyApp::Schema::Result::Lea
+gueTeam", "team" );
    __PACKAGE__->many_to_many( leagues => "league_teams", "league" );
    # ...
}

{
    package MyApp::Schema::Result::LeagueTeam;
    # ...
    __PACKAGE__->belongs_to( league => "MyApp::Schema::Result::League"
+ );
    __PACKAGE__->belongs_to( team => "MyApp::Schema::Result::Team" );
    # ...
}
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