Are there possessive suffixes whose position in relation to case/number suffixes can vary?

It is common for affixes to occur in a fixed order, however, it is by no means universal. Still, multiple orders do not necessarily have consequences for meaning (Lieber & Štekauer 2014: 376). The possessive suffix and the case suffix may be ordered in one way or the other, cf. Hungarian kutya-m-nak (px + case) vs. Finnish koira-lle-ni (case + px) ‘to my dog'. Still, in both languages their order is fixed, meaning that in Hungarian the possessive suffix always precedes the case suffix and in Finnish it always follows the case suffix. To compare, in Udmurt, there is variation in the ordering of the two suffixes depending on the case, e.g. with terminative and dative the possessive suffix comes before the case suffix, whereas in the illative and prolative it follows the case suffix (Kel’makov 2008: 77).

Coding. The value is '1' if the order of the possessive suffix and the case suffix can vary (as in Udmurt). The value is '0' if one of them precedes the other in all contexts (as in Hungarian and Finnish).

References
Kel’makov, Valentin. 2008. Udmurtin kielioppia ja harjoituksia (Apuneuvoja suomalais-ugrilaisten kielten opintoja varten, 14). 2. korj. p. Helsinki: Suomalais-ugrilainen seura.
Lieber, Rochelle & Pavol Štekauer. 2014. The Oxford Handbook of Derivational Morphology. Oxford University Press.