Not me, would be very lame, almost any sci-fi series have them as bad guys.. But true they could be very different from the original 3 races..

phase demons? lol what kind of ships would they have lol a flying skull??

- how about more classic: an antient race older and more powerful then the vasari

They (Vasari) are already an ancient and more powerful race than the youth of the galaxy.. (TEC and Advent), it would be funny to have another one even more ancient

I think it would be more along the lines of organic spacecraft.  Such as massive whale esque ships.

I would rather they have a few giant, imposing ships than swarms of teeny tiny ones. Just my opinion here.

I nominate this bad boy, alas, IskatuMesk will have a fit. This is truly a nightmare ship that comes out of a gas cloud and vaporizes everything in it's path before disappearing again...

Shivans. Gotta be.

Makes sense, if you follow the canon on Blue Planet: Age of Aquarius and the cut scenes in Freespace. The Shivans are the great destroyers/preservers. They bring balance.

Vasari are war like, aggressive (look what they did to Terran space).

Totally Shivans. >.>; 

There is also the culture thing. The Vasari experiment might have been about exposing dissidents to phase space and phase space interruptors technology. The result was a phase spacing hyper variant of Justin Bieber. He/it made the crews insane and the hyper rabid fans that he made possible gnawed on the ships until the point where they were so damaged that they fell apart.

More seriously. I think it would be interesting if the great pursuer isn't a physical menace and instead a culture based one. A bit strange there haven't been any theories about this because culture is an important part of Sins.

Culture is only really important when using the Advent from what I have found out.  But that's somewhat unrelated.

Maybe phase-space inversions?  It may be possible that some strange experiment tore the very fabric of reality...

But this is all just speculation.

You need something that has ships.. Or big "living" creaturesacting like ships to be able to put them into the 4th race.

Why does it have to be a race?

I think developers want this misterious thing to be the 4th race in Sins of a Solar Empire 2.. So it must have ship-like things.

advanced Orky Drones

Clearly the borg!
They would make great use of all those slaves!

Orky Planets, Advanced Orky drones, Mini Orky drones and nano orky bots.