FlyingExplorer, you mean a stopover in ICN (longer than 24 hours) rather than just a connection? Is this an award booking? On award tickets, KE permits one stopover on a one way along he routing, which would be ICN. The new KE website doesn't have an option for "multi city" bookings, which is what you'd need to book a stopover itinerary online. But if they did have that capability, it probably wouldn't be working. Since KE's website upgrade in Sept., it's been challenging if not impossible to complete an award booking online.
If this is for a paid ticket, the rules of a particular fare would apply. Some will permit a stopover, others won't.