Merge polygon pours in Altium Designer
I'm not aware of a function that lets you merge polygons.  At the same time, it's possible to achieve a similar effect while keeping the polygons distinct (without actually merging them).  


Make the polygons pour over each-other. No isolating gap between polygons that are the same net.


Right-click on the polygon pour.  Select Properties... at the bottom of the context menu.




Group the polygons.  Now they can be dragged around together.
To adjust the shapes of individual polygons, you would have to temporarily break-up the union.  You can't adjust the polygons while they are inside of a union.


Select the polygons which you wish to group. Right-click.  Select Unions → Create union from selected objects.