Q:

Make more internal storage available

I'm running a SlimKat ROM on Sony Xperia Z Ultra.  Officially the device has 16GB storage installed, but only 11.79GB are available to the user.  I know that all the rest is reserved for the OS needs.  May be the official Sony ROM really needs 3.5GB of space to function properly, but since SlimKat is a very compact ROM, I'm sure it doesn't need so much storage (am I right?).  
So is there any way to make more storage available for the user needs and less for the OS?  May be there are some ways to repartition the device memory.  
When I tried to google the question, I learned that there are some tricks to make the device treat the external SD card as internal storage, but that's not what I'm looking for now :)

A:

Yes.  It is possible to have more space allocated for personal use. 
First, I would suggest that your download Terminal Emulator and run the command df in it to get the memory allocated for each partition (ie /system, /data etc). 
The space allocated to /data partition is only space you can use.  Rest is for system/firmware that you cant use.  There are three ways to get out of this problem->
1) Repartition
We will reduce the amount of memory allocated to /system and give that memory to /data.  Manufacturers often give /system partition a farily good amount of space for future os upgrades.  But when you use custom roms, they are relatively lighter and use much less space, so we can shrink this partition.  But unfortunately, there isn't any such method made yet for xperia z ultra as far as I know.  So this is a rather difficult (almost impossible, considering working of sony phones, the TA partition etc). 
2) Installing as "system app"
You know that /system partition has a lot of unused space.  So how to use it?  Install apps inside system partition!  They will become system apps and you will need special app managers to uninstall them (you can use some app manager to install app and move it to /system partition.  Not all apps will support doing this).  Downside is that apps will still store their data in /data partition, so again, this isnt a very good option. ( You can also just create a random folder inside /system partition and probably store a few things like songs inside that?  Ok that might be a stupid idea, even though I do practice this on my Nexus 4, which has relatively even less memory). 
3) App2SD
This leaves you with only one efficient option as this.  Use some app like 
Link2Sd to move apps and their data to external sd card.  Hence more space inside internal.  Again, not all apps are supported, but most are.