Chosen Solution

I have Sony Xperia M4 Aqua E2303, can I change motherboard to E2333 or else, so I can have a 16GB ROM?

In fact yes it can be compatible with the phone in dimensions and all other specifications But there is one difference which is support 2 Sim So I do not guarantee full compatibility With your phone So I advise you upgrade to this model E2306 it have 16 GB Rom