I'm going to read your question strictly as "Are there languages that agree with their objects only with respect to plurality?" There are some cool examples of this. For instance, Classical Nahuatl usually has full agreement with both object and subject for both person and number. In ditansitive verbs, though, we cannot have full agreement with all three arguments. Instead, the verb agrees for number and person with the subject and indirect object and there is a suffix -im, which agrees with plural animate direct objects.
"Give me some turkeys."
If huehuexolo were singular or inanimate, -im would not appear. See The Syntax of Agreement and Concord by Mark Baker for more on this kind of phenomenon, which he calls two-and-a-half agreement because you can agree with two arguments and part of a third.
WARNING: The Nahuatl is missing some crucial diacritics that I do not know how to represent on the web.