LTM6622A: Second-Stage Filter for Switching Noise?

Hi, I don't use the LTM4622A, but with switching converters a good layout is paramount. Otherwise your whole ground plane gets noisy. This then counteracts all further filtering.
If your load is pretty constant, best thing is a LC-filter. With the inductor, keep an eye on the self resonant frequency.  Maybe you'll need a series damping resistor also.
Have a look on EMIFIL from murata or similar from other manufacturers

With additional ceramic capacitors, you have to consider that their capacitance is heavily voltage dependant. Choose one in bigger casing (eg. 1210). Or even better, parallel some smaller value ones.
Give them many vias in close proximity.
The 100µF will only be effective for lower frequencies. Polymer or special high frequency tantalum capacitors work best.

Thank you for your response, Alexxx.

Agreed on careful layout and power plane management.

Also note, I'm using the two outputs in parallel for multiphase operation (and reduced ripple), so the internal LCs are expected to be in parallel. I calculate 1.1uH of first-stage inductance.

Remaining Questions:

1. To determine an appropriate self-resonance margin for the second inductor, would we need to know the crossover frequency of the LTM662A, and put the LC resonance well beyond that? Do we know what this crossover frequency is?
2. If the required first stage output capacitance has to be 47uF x4, to achieve datasheet stated ripple, do you agree that the second-stage output capacitance has to be 4-10x that to prevent sensitivity to further capacitive loading from downstream bypass caps?
3. Seems like the EMIFIL series caps are more for low-current RF, whereas I'm looking for 2A power filtering at a cutoff frequency below the switching frequency of the LTM6622A (2.2 MHz)?