Adding an IDE controller card (like the promise) will give you addition IDE chains. The promise adds two more IDE chains for another primary master, primary slave, secondary master, secondary slave. So with a Promise card and your motherboard's chains you would have 4 chains for 8 devices using 4 IRQs since each chain uses an IRQ. At this point you will probably start sharing IRQs which most likely will not cause problems, but you may need to swap around the order of cards or the allocation of IRQs to slots in your BIOS if you do run into problems.
The one you pointed to is an Ultra 66. Promise also sells an Ultra 100. I don't think there is any real performance between ATA/66 and ATA/100 at this point. Promise also sells a FastTrack 66 and a FastTrack 100 IDE RAID controllers if you want to get into IDE RAID to improve performance. The Ultra 66 can be turned into a Fastrack 66 with a resister, a BIOS flash, and some fun with a soldering iron. If you are handy with a soldering iron this is a easy way to save some cash.