I can think of a being that is omnipotent. I can conceive of a being that is omniscient. I can conceive of a being that is omnipresent and even omnibenevolent. — lupac

All three of those traits have fallen under heavy criticism over the ages. They cause logical and moral conflicts and are far from being characteristics of a "greatest" conceivable being. I think a conceptual being which does not possess any of those traits is a vastly superior concept, as it is a far more practical conceptual form.

GCB +1

So it looks like it is good on paper and in practice.

I think some of you don't actually understand how subjective and shallow the argument laid out in the OP is, due to the way it is written I can always move the goal post.

I think a conceptual being which does not possess any of traits is vastly superior concept, as it is far more practical conceptual form. — Jeremiah

I do not quite understand what you mean here, but it seems like you are saying that the Greatest Being you can conceive of would NOT be omnipotent, or omniscient, or omnipresent. That seems to beg the question of what makes that being 'great'?
Simply because you can conceive of a Being that is not omnipotent, omnipresent, and omniscient and label that being "the Greatest being" means nothing unless the Being conceived has some intrinsic qualities that make it, by definition, 'great'. There seems to be objective, great-making factors that the Greatest Conceivable Being must have, or else we should revise our concept to be a Being that has those great-making traits. For example, let us say that lifting objects is a great-making trait. Everyone agrees that to be great, you must be able to lift an object. If I say, "the greatest possible being can lift a car over his/head" and you say, "the greatest possible being can lift a skyscraper over his/head" clearly the being you have conceived of is greater than mine. However, the concept of the GCB+1 ends because, eventually, it becomes clear that truly the greatest conceivable being must be able to move any object, and so we can all agree that unless the being we are conceiving of can move any object, it is not the Greatest Conceivable Being.
If you object to the idea that power, presence, knowledge, and goodness are 'great making' qualities, I am curious as to what you believe makes one thing better than another. But, as it seems obvious that there are great making qualities that people can agree on, we must the ascribe the Greatest Conceivable Being to possess those qualities to the qualities' greatest extent, and so there can be no GCB+1, as the GCB is then objective.

That seems to beg the question of what makes that being 'great'? — Ben Hancock

You are just now realizing this? The moment you read the word "greatest" you should realized that was an entirely subjective gradation.

The omni traits carry a slew of inconsistencies and conflicts, for a conceptual being to have a rational form, that humans can actually convince, it is far better just to forget about them.

f I say, "the greatest possible being can lift a car over his/head" and you say, "the greatest possible being can lift a skyscraper over his/head" clearly the being you have conceived of is greater than mine. However, the concept of the GCB+1 ends because, eventually, it becomes clear that truly the greatest conceivable being must be able to move any object, and so we can all agree that unless the being we are conceiving of can move any object, it is not the Greatest Conceivable Being. — Ben Hancock

So can your GCB make an object so big it can't lift it? Your entire argument is logically flawed, so your purposed GCB being is deeply flawed. Thus by limiting my conceptual being my GCB > your GCB, as with removing the omni traits it becomes more logically congruent.

Omni traits make for horrible conceptual beings.

So can your GCB make an object so big it can't lift it? — Jeremiah

I was mostly giving an example about how objective greatness exists, and mentioned nothing about God creating, but it seems that creation is also a great making property as you have so perceptively noted. The 'rock so heavy God can't lift it' is very easily solved by having a clear definition of what omnipotence is. The classic argument goes something like this:
1. Either God can create a stone so heavy that he cannot lift it or he cannot create it.
2. If God cannot the stone, he is not omnipotent
3. If God can create the stone, he is not omnipotent
4. Therefore, God is not omnipotent
I'm assuming that this argument serves as proof that

The omni traits carry a slew of inconsistencies, conflicts and for a conceptual being to have a rational form, that humans can actually convince, it is far better just to forget about them. — Jeremiah

Really, the problem here is just a misunderstanding of what omnipotence is. It would seem that God being omnipotent means He, by definition of being omnipotent, cannot fail. It would seem then, that God cannot create the stone not because he is limited in capacity, but because He is limited by the nature of being omnipotent. It seems at this point we are splitting hairs over definitional truths, but it is important to highlight that a GCB+1 who gains anything by being able to fail, is in no way greater than God described above. Even if you object to God being omnipotent in that scenario, it seems that a God who cannot fail then has some sort of great making property.
The basic point that people have been attempting to establish is that the 'Greatest' is objective. I am curious what you mean when you say

The moment you posted the word "greatest" you should realized that was an entirely subjective gradation. — Jeremiah

As it seems quite simple that any trait you identify, there is some maximization of that trait that makes greatest objective?

It would seem that God being omnipotent means[. . .] — Ben Hancock

So you are going to decide the limits of an all-powerful being? Really? That is some ego you have, but OK. So what you are saying here, is that humans have the power to limit and define the power of an all-powerful being. Which makes humans more powerful and thus humans are now GCB+1.

As an aside and for the record, humans are absolutely more powerful than God.

Jeremiah: "As an aside and for the record, humans are absolutely more powerful than God." Talk about an absurd claim. What God? Spinoza's God? How are humans more powerful than Spinoza's God? Or, a God that allegedly created the Earth 10,000 years ago and does not even exist since the Earth is closer to 4 billion years old? Or, the God that is supposedly existing as a supernatural being that governs the cosmos? How do we know that such a being does not exist? We can't know. Much less show rationally that humans are more powerful? We can't.

Hey, Mr. Wanna Be Scientists go prove your "fact".