Adding internal planes to the board doesn’t automatically reduce emissions. The amount of RF radiation from the PCB is proportional to the loop area of signals with high-speed transitions. The loop area of a signal is the path from the signal source to the signal receivers and back. Usually, the signal return path is through circuit common. By adding a ground plane over which the signal trace will run a capacitively coupled return path is added throughout the signal’s run length. This is why switching a design from two to four layers usually will reduce emissions. Other layout practices will also reduce emissions. Examples are don’t cross high-speed nets with nets connected to wires that go off the board, reduce signal path lengths, add a circuit common return net adjacent to the signal net, and there are many others. If you have specific questions or problems and would like to know more contact me.