«مَا جَاءَنِي غَيْرُ زَيْدٍ»
ghayru: nominative subject and first term of iḍāfa.
Zaydin: genitive second term.
«مَا رَأَيْتُ غَيْرَ زَيْدٍ»
ghayra: accusative direct object; Zaydin: genitive in iḍāfa.
These added examples show that ghayr changes with the governor while its complement remains genitive.