To start off, I'd take a look with a packet sniffer at what is going on. If you don't have Sniffer Pro or EtherPeek, go to www.ethereal.com where you'll find a great sniffer that's FREE. The help files and documentation are great also.
What you need to know is not just how many packets you have, but what kind of packets they are. If you have tons of ICMP, SNMP packets then the problem isn't with the switch, it's with your network (wasting bandwidth). You need to get a pulse for what's going on with the LAN...and the sniffer is the way. 15,000 pps to me is a huge amount for the number of users you have. I suspect you have devices that are "chattering" far more than necessary or even "rogue apps". Napster for example used to be the bane of admins everywhere for devouring bandwith and being extremely inefficient in how it did it - the old double whammy.
Have you done a baseline on you LAN? Take a look at it and the traffic. You may even want to monitor traffic over a weekend or late night to see what kind of broadcasts etc you are getting. It may be that your users send and receive massive amounts of data...but it may also be that there is a lot of wasted packets...maybe even a malfunctioning device.
If the LAN is fine andthe traffic is what you expect to have there (not a ton of broadcasts, unanswered requests, retransmissions etc) then the answer would be to add another switch, upgrade your switch or, better yet, to use a router (or bridge) to separate out the busiest parts of the network into separate collison domains.