The "Reshape Feature Tool" will let you change a selected polygon starting from anywhere. You select on the polygon you want to modify, click on the edge or vertex you want to start editing at, and reshape it. You have to close the reshape on the original polygon. This is probably as close to what you want as I can find. This will keep the attributes you may have entered for the polygon previously.
Add one vertex at a time. Select and then double click the polygon. The where you want to add a vertex, right click. I think you have to do this for ever new vertex you add.
I just discovered the "Replace" function. If I draw a polygon and finish it and then click the palet to start another polygon, select and right click on the existing polygon, there is an option to "Replace". This appears to do what you want, but two thing happen that you might not like. (1) The editing starts at the first vertex, not the last; and (2) it creates a new feature, it doesn't simply modify the first one. I'm not sure what happens to the attributes you may have entered for the polygon previously.
