You can add polygons to an existing polygon mesh using the Append to Polygon Tool. The Append to Polygon Tool creates the new polygon using an edge as a starting point.
To add a connected polygon to an existing mesh
The edge you select is the first edge of the new face. Arrows indicate the edge direction.
A new vertex appears with a line connecting it to the last point of the selected face edge.
If you want to append a face to a single non-boundary edge, use Edit Mesh > Extrude, then modify the new face as desired.