Visiting SLNP and LZNP, what does adding Kafue offer?

Hello! After visiting Tanzania, South Africa (Greater Kruger) and Kenya, we think Zambia is a great destination for our 4th safari! Mainly because we would love a good wild dog sighting. We are looking at visiting this mid September, 4 nights SLNP (Thornicroft or Flatdogs) and 4 nights LZNP (Royal Zambezi lodge). We are thinking about adding Kafue NP to the itinerary. But does Kafue add something extra compared to the other 2 parks? If yes, how does Kafue differ most? Is it worth spending 3 or 4 nights there? Or are we better of extending our stay at the other 2 parks? Would love to hear your thoughts! Thanks in advance. Kind regards