Experimentation with alternative tuning systems: Pythagorean tunings (which could be continuously adjustable in a computer), other ancient tunings, new ideas such as x-notes-per-octave equal temperament, etc.
Synthesize some ancient music using the tuning of the time period.
Experiment with inharmonic timbres based on some other tuning system.
Make a Max/MSP instrument that lets a person spatialize any sound according to a specified location or path.
Implement head-related transfer functions.
Make a Max/MSP instrument that enables you to chop up any sound and use its fragments as notes in a rhythmic structure (such as in a hip-hop groove).
Make a Max/MSP application that lets you modify sounds with real time interface control.
Make a Max/MSP sample player that lets you play back sound files at different speeds and/or with some modifications.
Make a musical composition that uses Max/MSP as the sole source, and that uses some innovative instrument(s) of your own design.
Implement a filter (using MSP, or using C to program an MSP object). (Requires reading the developer documents for those programs, of course.)
Make a usable "effects processor" (delay, flange, chorus, etc.) in Max/MSP (other than those found in the MSP Tutorials or examples).