Timing/distancing ("in phase") is one thing, another thing (I think even more important) is the feedhorn I guess.
A feedhorn expects an 'equal' field of signal, so to say, preferably with the highest density in the center.
So if you create more parabolic surface (by combining several offset dishes), but with holes in it; then from the holes you receive noise. (Unless you have a feedhorn with a shape, that matches the exact illumination by the parabolas.)
Adding a secondary mirror (cassegrain or gregorian) doesn't alter that.
So the effect is that you get more signal, AND more noise. So the S/N ratio result will likely be about the same as with just one offset dish, or maybe even worse.
When you want a bigger dish surface: Buy/make a bigger dish! All other solutions are troublesome, or maybe even worse....
Greetz,
A33