As far as I know, what Ultragames and I just explained does exactly what you want. From my understanding, you are wanting vertices to move together in a group only moving on a single axis at a time. You do not want the vertices to bunch up together in one tiny little group. Let me try to explain a little more what you need to do.
Image 1 - A sphere with some vertices selected.
Image 2 - The channel box at the right side of your screen. As you can see, it say "CV's (click to show). Click that and you get image three.
Image 3 - This is what the channel box looks like after you have clicked "CV's (Click to show)." As you can see, I have selected the Z axis box for vertice 119.
Image 4 - Scroll to the bottom of the channel box and shift-select the last box. All boxes become highlited. Type in a number, then press enter.
Image 5 - The result. All vertices moved together in a relative manner. If this is not what you are looking for, and would rather have all vertices move in an absolute way to a given position on the grid, go to image 6.
Image 6 - This may be what you are trying to do. All vertices are located on a single point on the grid. To do this, you must modify the settings for the move tool. Choose Modify>Transformation Tools>Move Tool (options box) This will bring up the options for the move tool. Under the "Move Snap Settings" tab, unclick "Retain Component Spacing" then click Close.
With you vertices selected, Hold down the x key (snap to grid) and move your vertices around a bit on each axis. All vertices will snap to the same point.
With "Retain Component Spacing" turned on, all vertices move relative to each other. With it unclicked, all vertices will move to an absolute position, but only when you are snapping.
I hope this helps a little.