Parallel coupling of piezoelectric
Assuming that all the discs are vibrating in unison then you won't need multiple LTC3588 devices. However, I'd be tempted to think about a series arrangement for the piezo discs. With two in series you will get twice the terminal voltage of one (at the same current) and, in some cases this will make an easier power conversion for the LTC3588 chip because the internal volt drop across the diode bridge will be a smaller proportion of the overall piezo voltage.

If you look on page 4 of the data sheet it tells you how much volt drop is incurred and it is largely a function of current and, having the piezos in parallel produces a bigger current at the same voltage.

For reference, page 11 says: -


  Piezoelectric elements can be placed in series or in parallel to
  achieve desired open-circuit voltages.