The Society collected specimens and sightings of creatures from higher dimensions. They had developed a taxonomy to classify all creatures. If their agents encountered anything that didn't fit, they would "simplify" it until it did.
Daniel Joyce's Advanced Research Project gave grants to the Society in exchange for "appropriate biological data" from their expeditions. One of these expeditions, partially funded by the Society, was Griffin's excursion to the temporal cicatrix in San Francisco in 2002. (PROSE: Unnatural History)