You can go on a rampage in Sleeping Dogs the way of doing this is you must have the Cop Upgrade that allows you to get weapons from the trunk of a Police car now find the nearest Police car and take a weapon from the boot. so now your packing some heat what you want to do is find some cover otherwise your going to die pretty quickly similar to GTA IV you can't just stand in the line of sight. So you have had a good few minutes of killing some Cops but your down to your last few bullets so what do you do huh? Well you charge at the nearest Cop like a freaking Rhino take his gun and find some cover, Rinse and repeat.
this may not appeal to some people but to me this sounds awesome it gives the Cop shootouts alot more of a challenge as it involves cover, bullet time or Slow motion as it's called in Sleeping Dogs, and strategy. Your not going to be sitting behind the same wall for the next five minutes you will be running out of ammo if you want to stay alive your going to have to take weapons from other Cops and run to there nearest car and take there Assault Rifle or Shotgun whatever you have at your disposal you must use it!
Although im not sure if there are weapon shops hopefully there are but if not there's still my method