To my surprise, there's not a whole lot of discussion on this very important topic. Anyone who has developed a custom remodel residential project can tell you it's not as simple, clean, or intuitive as a custom new construction residential project.
The first step is pretty staight forward... build your as-built model in the existing phase. Once an as-built model is done you might want to archive a copy of the model just incase the design scope changes and you have to start all over again with a clean as-built. Now I'm sure you are all aware that as the design develops the project architect and the client are both going to want to explore varying design iterations. The model builder is going to have to do partial demolition of walls, floors, roofs, ceilings, etc. The way most Revit Beginners go about doing this is to split the wall, floor, roof, etc into two parts and demo the half they want to remove. The problem with this method starts to reveal itself after 2-3 design iterations when the as-built model, now split into many parts, degenerates into useless plans and elevations. Constantly reshaping the proposed design on the fly without time consuming cleanups also becomes less possible.
So what do you do with partial demos? You could create a new phase between Existing and New Construction called "Existing To Remain." Then copy the element to be demo'd to the clipboard... then demo the whole element in the "Existing to Remain" phase... paste the element (into the same place) back into the "Existing to Remain" phase and then reshape the existing to remain version of our element (Some users think that a demo phase is not necessary, but it has it's benefits). Now anytime the design goes through iterations all you have to do is reshape the existing to remain element while leaving the as-built model preserved and intact.
Plans require additional cleanup, but this approach reduces the frequency and types of cleanups required, particularly obvious when you move on to elevations and sections.
EDIT: Partial additions can be done the same way you would do partial demos... copy, demo, paste, reshape. If you just add on to the length of a wall you're going to end up with a proposed design that's in pieces too. This can be important later on down the line when you want to combine phases into a new asbuilt. However, getting accurate Material Takeoffs on a remodel can add a dimension to this procedure (you might want a model that's divided into accurate pieces afterall).
EDIT: This process works with or without a demo phase. The critical point is to group and pin previous phase work before proceeding with the next phase and then copy, demo, paste, reshape in the next phase... with plan cleanup in demo and proposed plans by regions and element overrides. Most beginners only think in terms of existing and proposed. This process considers multi-phase projects.