Is it possible to use the DJM-S9 as a general purpose MIDI controller and to operate MIDI-compatible DJ software other than Serato DJ?

Operation is possible. When using DJM-S9, pay attention to the following points.

(1) DJM-S9 automatically switches to the "mode optimized to Serato DJ" when Serato DJ is running and to the "general purpose MIDI controller mode" when Serato DJ is not running.

(2) In order to operate the MIDI-compatible DJ software with DJM-S9, the various operating interfaces of DJM-S9 must be assigned to the various functions of the DJ software.
For details on assigning the interfaces, see your DJ software's operating instructions.
The operation instructions can be obtained from the following Pioneer DJ site.
DJM-S9　Manual