Just a hunch, but the total load that all of the phones creates is probably exceeding what your service provider can support (the maximum R.E.N. limit is being exceeded).
A simple test is to unplug all of the phones, connect one make a test call in, add another phone and repeat until the phones no longer ring properly.
But, yes, are you getting service from a cable provider, Verizon FiOS or Verizon copper?
