Core switch(es) - what do you have plugged in?
This may sound like a daft question, but what have you got plugged into your core switches?
Apart from the obvious connections, such as servers, switch uplinks, links to remote network cabinets, WAN & WLAN links what else have you got plugged in?
I am looking at our core switches (2x HP3500-24G) & I find the people who put the network together have got UPS management & DELL Server DRAC links patched in as well as all the normal stuff. These are taking up almost as many ports as the servers. Given that the core switches & all the others in the rack are protected by UPS is there any reason for them to be in the core switch?