Nope, you're stuck with the 2 onboard processors, period. (Well, some recent Rolands & Yamahas have 3, but Korgs are MUCH more friendly to use, as a rule. Not ALWAYS, but usually. Everybody makes a few good things now.) You CAN route your Korg sounds to different outputs, (on the instruments in their line that have 4 or 6) & use the effects as 2 separate creatures, obviously, but otherwise, your only choice is to program some of your tracks VERY carefully so they'll be useful dry or add an outboard FX box or 2. (Try the 'dry' route; it makes for some good learnin'.)
Also, several recent processors allow you to divide their arsenals into 2 units that further extend your choices, so check out Digitech & Lexicon, who are two of the better companies in this area. Virtually all of the current software (Cubase etc.) is good at letting you assign different FX to different channels, but in some cases, you have to buy a "breakout box" to get the extra outputs required to make this a more reasonable prospect. The channels are in the software, but only available in this manner. I know its a bit disheartening when the answer always seems to be "buy another box," but at least one outboard FX unit is almost a must, as it can cure a lot of ills at tight moments. Don't be afraid to try this: its not a POD & the rewards can be spectacular. Check out the 2nd-hand outlets for a mid-line FX unit, such as roguemusic.com or ugbm.com. They've both treated me well & have online catalogs. Good luck!