On Windows this is configurable up to a maximum of 8 channels by changing the settings in the DIRECTOR.INI (or PROJECTORNAME.INI) file -- the default setting for Director is (I think) 4. If you want to use more, you must first change the .INI file and restart Director.
On the Mac, the number of possible sound channels is limited only by available RAM and processing power (most Macs perform sound-processing internally instead of delegating much of the effort to a sound card as on a PC). Some developers have used as many as 16 simultaneous sound tracks.
In general, however, the more simultaneous sounds you use, the more demanding your movie will be on system resources. It's usually best to try to minimize the number of separate sounds that have to be played simultaneously. For most purposes, four channels is reasonable limit.