QGIS alone does not provide handy tools for aggregation of features of one layer combined with other layers, but the spatiaLite engine is tailored for this! Since QGIS now makes import/export and querying of spatial data easy, it seems very worthy to dive into spatiaLite and utilize its powerful tools!
For the presented example I'll use:
I tested this on
SELECT t.geom AS geom,
t.plgnID AS plgnID,
t.soiltype AS soiltype,
max(t.soil_area) AS MaxArea, count () AS n_soiltypes
FROM (SELECT
g.Geometry AS geom, g.plgnID AS plgnID, s.Soiltype AS soiltype,
AREA(INTERSECTION(g.geometryO, s.geometry)) AS soil_area
FROM SHAPE1 AS g JOIN Soils AS s
ON INTERSECTS(g.Geometry,s.Geometry)
) AS t
GROUP BY t.plgnID
ORDER BY t.plgnID
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