If you have access to a plumbing snake (or can purchase/rent one), it can be an effective tool for reaching and breaking up clogs further down the drain.
Sometimes, a combination of dish soap and hot water can clear a clog. plunge sink without plunger
Hair, often mixed with soap film, creates “drain snakes” that act like a net. A manual hook can pull this mass out. If you have access to a plumbing snake