In this graph Multigraph uses an alternative scheme for processing mouse events, known as the "Nearest Axis" scheme. In this scheme, there is no concept of "selected" axis. When you click the mouse and start to drag, Multigraph assigns an "orientation" of either vertical or horizontal to your dragging motion, based on the direction you start dragging in. It then finds the axis of that orientation (vertical or horizontal) that is closest to the point where you first clicked, and uses that axis for panning or zooming, until you release the mouse button.
Every time you click and start to drag the mouse, Multigraph goes through this process again to determine which axis to affect, based on the location and direction of your first dragging motion. It is therefore important that your first mouse motion after clicking be in the direction you intend --- be sure that you don't accidentally bump the mouse in the wrong direction as you click. Once you start dragging, the choice of axis is locked until you release the mouse.
So, for example, if you want to affect a particular vertical axis, click anywhere in the graph that is closer to that axis than any other vertical axis, and drag vertically. To affect the horizontal axis, click anywhere (at all) and drag horizontally. (If there were more than one horizontal axis, the same "nearest axis" rule would apply; but most graphs have just one horizontal axis.)
As in the "Selected Axis" scheme, hold down the SHIFT key to zoom instead of pan.