Synonyms for on

1. Upon

   above, in contact with, touching, supported by, situated upon, resting upon, on top of, about, held by, moving across, moving over, covering; see also upon 1.

   Antonyms under*, underneath, below.

2. Against

   in contact with, close to, leaning on; see against 2, next 2.

3. Toward

   proceeding, at, moving; see approaching, toward.

4. Forward

   onward, ahead, advancing; see forward 1.

5. Near

   beside, close to, adjacent to; see bordering, near 1.

and so on

have something on someone*