First and foremost, dump that Niles Speaker selector. The passive volume controllers of this type are cheap and commonly used, but are not the correct way of setting up a multi-room audio distribution. More on a better way to do this later.
Don't worry about the power rating so much as the fact that the LSI9 are pretty demanding load. The impedance and phase from
these measurements shows that they will definitely benefit from a good amp.
In terms of how much power, using Sensitivity of 87dB/W/m, keeping LSI9 within 2 ft of a wall, and at a listening distance of 10 ft; using an online SPL calculator, one can see that feeding a pair 100W will give an ear bleeding 106 dB SPL.
If your Yamaha receiver has a pre-outs, you can use something like this
Rolls Distribution Amp (in place of the Niles Selector) to split the signal into 4 identical stereo signals. If not, you can connect the CD player directly into the Rolls input. It also has a 1/8" headphone input to temporarily connect any portable devices like iPods.
Now you put the outputs of the Rolls DA into 4 stereo amps with built in volume control. Why do you need an amp with volume control? Because the level knobs on the Rolls DA are not "volume" knobs. Instead they are a one time set and forget knob to match the output level with the input sensitivity of the amp inputs. This is used to insure that you will not clip the amp inputs.
Now, for the amps to power your LSI9, the
AudioSource Amp 110 is rated for 110W into 4 Ohm loads and will be perfect. I did not see which speaker you have as the third set, so hesitantly I would say that the Amp 110 will work for them too.
The beauty of this approach is that in the future, if you swap out a LSI9 pair for something needing more power, you only need to change the specific amp feeding that set.
