Using my last international trip as an example, I brought scrub bottoms to change into on my long-haul/lie-flat flight segments, and had two changes of shirt/underwear to use after my two showers along the way (after each leg).

My international trips can be a 24-hour travel experience, with two multiple-hour connections. The best use of the transit time is to clean up. The shirts/underwear take minimal space in my carryon.