work on someone
1. . Lit. [for a physician] to treat someone; [for a surgeon] to operate on someone. The doctor is still working on your uncle. There is no news yet. They are still working on the accident victims.
2. . Fig. [for someone] to try to convince someone of something. I'll work on her, and I am sure she will agree. They worked on Max for quite a while, but he still didn't agree to testify.
3. Fig. [for something, such as medication] to have the desired effect on someone. This medicine just doesn't work on me. Your good advice doesn't seem to work on Sam.
work on something
to repair, build, or adjust something. The carpenter worked on the fence for three hours. Bill is out working on his car engine.
work (up)on something
1. . to repair or tinker with something. (Upon is formal and less commonly used than on.) He's out in the kitchen, working upon his tax forms. He's working on his car.
2. . [for something] to have the desired effect on something. (Upon is formal and less commonly used than on.) This medicine should work well upon your cold. I hope it will work on your cold.