Many to many to many relationship ?

You can use an extra column in the pivot table to set the role_id between the game and the designer. However, it's not possible to set this up as a real relationship between game and role or designer and role. You can create a pivot model and add the relationship in there.

class DesignGame extends Pivot
{
    protected $table = 'design_game';

    public function role()
    {
        $this->belongsTo(Role::class);
    }
}

Then in your code, you can do this:

$game = Game::with('designers')->find(1);

$game->designers->first()->pivot->role;

This should put you in the right direction

Finally, you can add a unique constraint on all three columns to make sure they are always unique.

Schema::table('design_game', function (Blueprint $table) {
    $table->foreignId('game_id')->references('id')->on('games');
    $table->foreignId('designer_id')->references('id')->on('designers');
    $table->foreignId('role_id')->references('id')->on('roles');

    $table->unique(['game_id', 'designer_id', 'role_id']);
});

Note that the above code is the new Laravel 7 syntax for creating a column including foreign keys in migrations.

Thanks for your answer. I will test this.