How much power can a 74HC4066 switch (for LEDs)
To answer your question with your current approach (total current sink capacity), you will have to pay attention to the safe operating area (SOA) of the device. The datasheet you referenced has different 'on-resistance" (RDS_ON) for various operating points. 

I would say that the current would not share exactly equally if you would like to switch one main bus with multiple switches in parallel. 

For higher currents, I would recommend a logic-level MOSFET, which have Vgs_th of 1-2V, so a microcontroller with 3.3V logic levels can drive the gates easily. 

The advantages are
1. It is smaller (you can find an N channel logic level MOSFET in a SOT-23 package)
2. You can carry more current than 25mA (typically in the hundreds of mA).