PCB stackup for capacitive buttons, LEDs and other components
The amount of layers shouldnt matter, as long as you carefully control the capacitance seen by the buttons. If you can control the capacitance from the top layer sensor pads and their traces, to the nearest reference plane, then you should be safe to do whatever you want bellow that plane if i am not mistaken (keep in mind, this recommendation is not based on experience!) as the capacitive coupling will be primarily to the first reference plane. 

You also need to be very mindful that the buttons and their traces are a EMC hazard and they are sensitive to parasitic coupling. All your digital stuff has the potential to send you back to the drawing board when your board fails EMC testing due to coupling into the sensor pads. 

I have done a 4 layer capacitive design before, but no extra electronics except level translation, I2C and some LEDs. But i remember the LEDs toggling on and off shifting the measurement levels of the sensors visibly, so sensitive were they to EMI. 

If i was going for a 6 layer stackup. I would consider this one (up for scrutiny here). 

-Sensor pads + traces

-Reference Ground (Sensor ground)

-Power

-Signal

-Ground

-Signal

The reasoning is that the first two layers establish the pad capacitance, the next power layer provides isolation of digital signals against the sensor pads by holding any digital return currents that might otherwise flow on the sensor ground. This stackup also fullfills having reference planes close to any digital signal layers. This is what i would personally start with.

The main issue with adding layers is that the average distance between them gets smaller and smaller, you might need to design the layer stackup to really sqeeze the inner layers together, to get the needed separation between the sensor ground and the pads, while still maintaining a symmetric stackup as asymmetric ones are really really unpopular for many reasons.