To integrate more international tournaments into the storyline of Haikyuu!!, the creators could introduce new rival teams from various countries such as the United States, Brazil, Italy, Russia, and other volleyball powerhouse nations. This would allow for exciting matches between different playing styles and strategies from around the world. Additionally, they could incorporate a plotline where the Karasuno High School team competes in a prestigious global volleyball tournament, showcasing their growth and skill on an international stage. This would not only add diversity to the series but also provide new challenges and opportunities for character development.