Since each series in a scatter plot is an adjacent x-y column pair, it isn't possible to arrange two series in such a way that the series share an x column but have distinct y columns (you can, for what it is worth, have two series that share a y for one and an x for the other... see below).
That said, this is not hard to work around. Simply introduce a second x column to the left of the second y column. If, for example, the shared x is in column A, fill this this new column with the formula =A which will create a copy of the shared x which can be used to pair with the second y for the second series of the scatter plot.
While on this topic, let me point out a related, I think, non-obvious thing about the series of a plot. In the case of a two series scatterplot, for instance, the two series don't need to be adjacent (the x-y pairs
do have to be adjacent, I think). To arrange this, select the two pairs of columns containing the data for the two series. Since they are not contiguous you can use cmd-clicking to make discontiguous selections, then create the scatter plot.
It also is possible to move around the source ranges for each series independently. Here the trick is to select the points in one of the series in an existing plot by clicking on one of its points in the plot. You have done this correctly when you see a circular selection indicator in each of the points in the series. This will also highlight the series' cells in the source table. By grabbing the border of the source cells, this can be dragged around to a new set of cells (or, oddly, even overlapped with the other series).
