The number you can drive depends on the clock frequency you expect to run it at. The clock input pins on each BBD have input capacitance. When the total capacitance is summed (it's all in parallel), the result is that it corrupts clock pulses from the 3101 above some given frequency. Think of that input capacitance as being like a fixed lowpass filter on the clock pulse. As long as the clock stays well below the corner frequency of that filter, the clock is received exactly as sent. Round off those rising and falling edges with the input capacitance, and the switching action within the BBD*becomes less seamless and contiguous, resulting in a serious decline in audio quality.
The traditional workaround is that a buffer, which serves as current driver, is placed between the BBDs and whatever is being used as clock source. As the drive current of the clock signal increases, the BBD becomes more capable of accepting higher frequency clock pulses without the input capacitance causing a problem. I have it on good authority that you can clock an MN3007 (which Matsushita datasheets depict as crapping out around 100khz....without buffering) well past 1mhz.