1980's Inferno , Dario Argento's very next movie after Suspiria was not just a sequel - a sequel that had not by any means suggested itself from the plot of the first film, mind you - but a film that went as much deeper into complete, deliberate incoherence as Suspiria had done to the gialli that were Argento's stock in trade throughout most of the 1970s.
Then he took a turn into supernatural horror with Suspiria in 1977 and scored his biggest hit in the United States, where it was released by 20th Century Fox (under a subsidiary label).
This passage seemingly explains the events that transpired in Suspiria —the witches at the Tanzakademie called on the strength of Helena Marcos in honor of Mater Suspiriorum—while setting up the events of Inferno and the yet to be produced Mother of Tears (which, according to Daria Nicolodi, has been ready to film since 1984).
Ultimately, I think it's fair to wonder whether Argento has as much to do with the success of the four movies (Deep Red, Suspiria , Inferno, Tenebre) he made during this time as some divine (and brief), Rilke-ian wind.
These bravura displays of technique remained at odds with his banal handling of actors and narrative, but his best known film, Suspiria, seemed to indicate that Argento had begun to devise a style of commercial film-making which was moving away from the limitations of conventional narrative (or certainly treating it in the most perfunctory fashion), and thrilling the audience only through sound, image and movement.
Unfortunately for her, the Akademie turns out to have been founded by one of the Three Mothers, immortal female monsters (who also pop up in Argento's film Inferno) and Suzy is led deeper and deeper into a maelstrom of potentially deadly secrets.