If what you want is to bypass the floating inaccuracy caused by single point precision problem, for the sake of creating bigger environments for your game, then it depends on what you are willing to accept as a solution.
Let's start by making this clear: it is impossible to alter the coordinate system at the inner core of Unity. So, you can't use double-precision inherently for coordinates.
1) Depending on how you need it, however, it is possible to have custom classes in double-precision that might be of help. Of course it sill converts back to float so Unity system can work with, which is not a solution, but in many cases it might be of help even if for implementing other solutions. By the way, someone has already implemented that for Unity: a fake Vector3d, i.e. a fake Vector3 with double precision: https://github.com/sldsmkd/vector3d
And for a discussion on that piece of code, please see: http://forum.unity3d.com/threads/double-precision-vector3.190713/
2) As for the second part of your question, yes, it is possible to divide the world in areas to bypasse the problem for having big environments. But that still uses Unity's usual single precision coordinate system. That trick was first implemented in the game Dungeon Siege. The guy behind that wrote a paper on it:
And also gave lectures about it too, from which slides are here:
There is a video from a couple of years ago, where people from Unity comment on that solution and even explain a modern implementation of the concept in Unity:
Also, there was already a similar question in Unity QA, with an user answer that might also enlighten you on the small piece related to coord-conversion:
3) Also, see this blog entry, with very interesting stuff on the problem and an idea on using multiple cameras to handle it
4) Lastly, there is also the now famous solution implemented by Kerbal Space Program, which was a game made with Unity. It is not a new solution and is sometimes refered to as "Futurma method", being related to a broader solution called "floating origin".
First of all, see this general discussion on your problem with a related idea using offsets from the player position:
Specifically on Kerbal, you can see:
And also: https://www.youtube.com/watch?v=mXTxQko-JH0
For a good (although non-professional) tutorial on how to implement it:
And for a script implementing Floating Origin in Unity, see:
Lastly, a definitive must-read is the following paper, which proposed the Float Origin years ago and even describes and compares it to the other solutions such as dividing space into chunks with their own coordinates: