Hello Jon,
Yes -- you can do that by using Hauptwerk's built-in recorder to record the parts as successive MIDI files, overdubbing them with each iteration. When you're happy with the finished result, if you wished you could then play back the MIDI file in Hauptwerk's MIDI recorder/player, whilst simultaneously recording to audio.
The 'Recording menu' section in the main Hauptwerk user guide (on the Help menu in Hauptwerk, pages 132-136 in the current v4.1.1 version) covers those things, and the 'Overdubbing MIDI recordings' sub-section in particular.