On the surface going by the diagram, I would imagine you could phase things relatively easily. In essence, the only "big" bits that appear to be happening are that the platform 2 line is being removed and the platform built out to meet the platform 1 line from the other side (and the platform lengthened westwards), and platform 4 being extended over the access to platform 5. Other than that, it's just changes to pointwork (and obvs. the signalling).
So at the start, close platform 2 and have everything heading west use platform 1 for the duration, close platforms 4 and 5, redirecting services to platform 3. That gives you two usable through platforms whilst you build out platform 2 and lengthen platform 4.
Once platform 4 is lengthened, flip services from 3 to it, and make the changes needed to cut the link on the eastern end. Once 2 has been built out, close 1. Then resignal everything.
Really doesn't sound like a two year closure's worth of work...? Unless they just mean weekend closures or some such, which would make a lot more sense.