Bingowings said:

Building more Death Stars makes sense.

If the Soviets had destroyed the fourth Nuke the US would have built three more and probably have used them too.

Two Death Stars would have been better but a whole cluster of the buggers would have been better still.

It would be like the Emperor saying, "Well done little Alliance, you blew up the first of my Battlestations, now try blowing all these up!"

Even if the Rebels had failed at blowing the first one up I'd imagine the Empire would have built more.

Realistically, yes

Cinematically though it looks a bit dull just to have another one that isn't even finished.

I personally disagree, though I respect your opinion. There's something I like about the two different designs (as they do look significantly different). My personal wish is that we only were able to see different faces of the DSII instead of always the same side.

That's why I suggested that the Emperor feed the Rebels the location of an unfinished one when he already has a finished one, but both are fully functional.

I too like this idea.

Other designs would have been interesting too.

Another obvious possibility for the Sequel trilogy is what does the New Republic do with this technology.

Do they make their own for defense knowing that someone else will eventually make another one?

An interesting moral dilemma for a less black and white trilogy :)

The EU in the early days was full of superweapons and that became boring very fast.

I will agree with you completely and then some.