Saarinen Oval Dining table base question.  

I was looking up the Saarinen sizing of the oval dining table and the only thing that's different is the height. I'm wondering if there was this second layer added to raise the table.

There are a lot of genuine Saarinen tulip tables listed on 1stDibs and quite a few include photos of the underside of the tables. I could not find any that had even close to the number of screws yours has (though someone could have added screws at some point, I guess). But more importantly, I could not find any that had that groove or joint around the perimeter of the top of the base that yours has. I'm hardly an expert on these tables so I don't know the significance of that, but I do know that they were widely knocked off over a long period of time so I tend to think that yours is probably not genuine.
You could also take a photo of the base from straight on against a plain background and compare the radii of the curves, and the diameter of the stem and top and base to the photos of the real thing from a licensed distributor or Knoll. Many knockoffs look pretty convincing until you compare them side by side, and then you start noticing little differences in the shape.

To me, it just looks like someone wanted it to be higher than the normal 28.25 and got an extension, but who knows..

Do you have an overall photo of the base shot from straight on? How about a shot of the underside of the bottom of the pedestal? That might help to figure out for sure if it's real or not.
I get what you mean about someone wanting to add height. Is that layer just atop the base the same material as the other layers? I assumed it was part of the pedestal until I looked at it again just now. I see that the color is the same warmer white as the other layers above it. But it's so perfectly sized to match the pedestal top---just odd! But possible, definitely.

Here is the full table. I'm solo right now so i can't flip it over. That said, I did see in there and there were no marking. There was a large allen wrench nut that would be running through the base though.
The 2 layers of the base attachment are the exact same in every way, just one is on a larger scale. I just wonder if there was ever the option to have it heightened. Either way, still a solid table.