ἑκάστην δὲ γένεσιν ἄλλην ἄλλης οὐσίας τινὸς ἑκάστης ἕνεκα γίγνεσθαι, σύμπασαν δὲ γένεσιν οὐσίας ἕνεκα γίγνεσθαι συμπάσης.
How to understand this ἄλλην ἄλλης? each instance of generation is for the sake of a certain being, one for the sake of another.
What a nice little turn of phrase! Without the ἄλλην ἄλλης you wouldn’t know that each ἑκάστην was necessarily different from each ἑκάστης. This is a wonderfully clear and compact way to put it.
If I were going to translate it, instead of making them separate, I’d combine in English with something like: Each individual genesis comes about for a different individual oysia of something.
[Note: I still haven’t read Philebus and haven’t looked up the context beyond your post, so I could be wrong, as always.]