I would guess you can't 
or at least it would have to be checked out first by Sony.
Hi marjanasil
Welcome to Club vaio, 
Unfortunately it clearly states in the warranty terms and conditions that you must register within a year of purchase at the VAIO-Link Call Centre for assistance from our team.. 
You could check this with Vaio-Link but make sure you check before you purchase the cover... 
Hi there. I don't think it's possible to extend the warranty, once it's original has expired.
If I am not mistaken, you should have done this when you bought your notebook (was there a choice of extended warranty?), or while the original was still valid through SONY.
But then again, it's quite a long time since I got mine, so things might be different now
