He sang in the first German-language Don Giovanni (Mainz, 13 March 1789), produced or conducted other operas by Mozart, Salieri, Gluck and Gassmann, composed incidental music (e.g. to Bürger's version of Macbeth, 30 August 1785) and acted in dramas by Lessing and Schiller.
The summit of Stegmann's activities in Frankfurt was the production of his allegorical Singspiel Heinrich der Löwe (15 July 1792) to commemorate the coronation of Emperor Franz II.
By the time of his return to Hamburg in November 1792, he was esteemed as a leading operatic producer and adapter, which compensated for the declining vocal prowess that forced him to restrict his appearances to comic roles (Allgemeine Musik-Zeitung i [1798-9], col. 713).
In 1798 he joined the directorate of the Hamburg theatre, remaining there until 1811; thereafter he moved to Bonn and attracted attention mainly as a composer of incidental music and a series of instrumental works (Allgemeine Musik-Zeitung iv [1801-2], col. 261), including keyboard and multiple concertos.
As a composer for the theatre, Stegmann has attracted attention for his harmonic and tonal organisation and for using antecedent forms of leitmotif, showing an early interest in dramatic and psychological continuity.