In forms like Claudio's house or Claudio's dogs, are there languages in which the Claudio's would change depending on gender and number of the houses or dogs?
In Romani, the genitive case marker looks something like -kVrV or -gVrV, where V depends on the gender (and I believe number) of the object. So for instance, you have
me phral-es-kere kher-es-koro vudar my brother-OBL-GEN.NEUT house-OBL-GEN.M door 'The door of my brother's house'
where kher is neuter and vudar is masculine.
In most Grassfields Bantu languages of Cameroon, there is an associative morpheme which agrees with the possessed noun in a genitive construction. In the most minimal type of agreement, the associative marker is a floating low tone for noun classes 1 and 9, and a floating high tone otherwise. Noni, a Beboid language, has eighteen different genitive markers, depending on the noun class of the possessed noun (Hyman 1981: 19).
A mixed case is Nkwen, of the Ngemba group of Grassfields, which has a segmental genitive marker for classes 2, 5, 6 and 19 (agreeing with the possessed), a floating low tone genitive marker for classes 1 and 9, and a floating high tone marker for other classes. (Ncheafor 2002)
Your question doesn't specify whether you are interested just in nouns or also in pronouns or adjectives.
In Spanish these forms of the possessive/genitive adjectives/pronouns (terminology depends on analysis/tradition) are inflected for number, and some also for gender, to agree with the possessed rather than with the possessor:
- 1s: mi / mis
- 2s: tu / tus
- 3s/p: su / sus
- 1p: nuestro / nuestra / nuestros / nuestras
- 2p: vuestro / vuestra / vuestros / vuestras
This is common among Romance languages.
Most Slavic languages have such inflection form. It applies both nouns and pronouns and both possessor and possessed inflect in agreement.
My samples would be in Ukrainian.
Pron. 1st: Я
Son (noun, masc.): син
Daughter (noun, fem.): донька
"My son" (nominative/genitive/dative, other cases skipped):
мій син / мого сина / моєму сину or моєму синові
"My daughter" (nom./gen./dat.):
моя донька / моєї доньки / моїй доньці
Plural form: "my sons and daughters":
мої сини та доньки / моїх синів та доньок / моїм синам та донькам
Nouns (possessor) are inflected in a similar way:
Ivan (prop.noun): Іван
"Ivan's son" and "Ivan's sons" (nom./gen./dat.):
Іванів син / Іванового сина / Івановому сину
Іванові сини / Іванових синів / Івановим синам
"Ivan's daughter" (nom./gen./dat.):
Іванова донька / Іванової доньки / Івановій доньці
There's yet another way of forming possessive by placing the possessor at the end. This way, only possessed inflect while the possessor remains in genitive case only:
син Івана / сина Івана / сину Івана
One could imagine that genitives agreeing with both object and subject represent a transition stage from genitive (as a case only agreeing with subject) to adjective. Cf. German Grimm’sch, alternative spelling grimmsch, where Grimms Bruder/Schwester only agrees with Grimm, but Grimm’scher Bruder is also congruent with obj., different from Grimm’sche Schwester and * grimmischer Bruder would only agree with the object of the genitive relation. The difference between these forms would be if one would like to focus more on the subject or the object, grimmisch making Grimm more abstract than "Grimms..."