Why do I have multiple connections on a single common connection?
The wiring in the switch box isn't only for the switches.  It is also carrying supply power onward to other points of use.  That is the reason for the extra wires coming off COM. 

This would be easier to understand if the 3 brown wires you drew terminated in a block just like the neutrals, and then 2 pigtails from the block went on to feed the two switches on their COM side.  

Pretend it's like that, or get blocks and pigtails and make it actually like that.