Translation:Do you know anybody who drinks more coffee than him?
As per earlier exercises, "...than he" needs adding as it is correct English.
Reported, mentioning here for non-native English learners.
1) "...than he" is prescriptively correct English (just like in Polish; we're comparing subjects, not objects)
2) That said, "...than him" enjoys popular usage regardless and can be described as still descriptively correct, so should also remain in the database.
I think such situation is possible. For example, when you see that someone is drinking more coffee than he is, and you want to know this person. Although such situation should be rare, because drinking much coffee during a short period of time is life threatening.