How many units may I put on one 15 amp breaker?

It depends. Since an individual unit of The Director may draw a maximum of 1300 watts and you are limited to 1500 watts per device by most codes, there should be a separate 15 amp circuit for each. Optionally, you could squeeze two units onto a 20 amp breaker and be very close to the limit at 120 volts.

The circumstances where The Director draws maximum power are very rare outside of an engineering lab. Maximum power is using a sine wave input which has at least a third higher energy density than music. This would mean that all channels are operating at maximum, an unlikely situation even during a really fun party. Even more unlikely is all channels on multiple units operating at full output.

You know the system better than we do, so it is your decision. If the only use is background music, then the one-eighth power in the specifications at the end of this manual is a reasonable (actually conservative) power draw. Of course, you will want to include a margin of safety for unusual circumstances. And in the final analysis, you have to do what the electrical inspector tells you to do.