The manner in which the Habsburgian collections were organised, also changed during the time Stütz was in office. Thus, besides
the "old natural history collection", located in the Augustinian tract of the Court Library, which Stütz had to administer,
there was also the Physical-Astronomic Cabinet, the Arts-Cabinet and the "Natur-Thier-Cabinet" (Nature-Animal Cabinet) at
Stütz assumes their management temporarily in 1801, after the death of Ludwig von Baillou, whose son renounced the directorship willed to him by Franz Stephan von Lothringen, the collections are combined and Stütz appointed as sole director in 1802.
He is assisted by Johann Baptist Megerle as assistant director, alongside the custodian Johann Carl Megerle. From 1786 onward, the latter carried out work on the organisation of the Natural History Collection on an honorary basis, was made assistant custodian and in 1797 custodian. The title of the new museum is now: "Vereinigte Naturalien-, Physikalisches und Astronomisches Cabinet" (United Natural History, Physical and Astronomic Cabinet); it exists from 1802 to 1806, when Stütz dies, 59 years old. Minerals, rocks, precious and ornamental stones and fossils as well as several meteorites are assigned to the "Mineral Cabinet".