If I read your question correctly, you are interested in staying in Murchison Falls NP for a couple of extra days after the Chili tour of MFNP is finished. This is, of course, possible, but...
Here are the main things to do in MFNP:
1. Go the falls and be amazed at the power, take some short hikes around to get different views of the falls. This could take between 1-3 hours depending on your speed and how long you like to absorb the beauty or watch birds, etc.
2. Take a boat launch at Paraa to near MFNP and look at the animals and birds along the way. These happen in the morning and afternoon.
3. Take a 'safari' ride in a vehicle north of the Nile River and watch for animals (elephant, giraffe, kob, lion, waterbuck, etc., etc.).
Now, with the Red Chili tour, you do all of these. With their transportation, they take you to the falls and they take you across the river on the game drive, you also take the boat launch once as well. If you stay afterwards for a couple of days, here are the things to think about.
- You would need to book additional reservations at the Red Chilli restcamp or at one of the other three hotels in the park which are much more expensive than the Red Chili.
- Determine how you would get transportation to do whatever it was you wanted to do during the extra days. If you wanted more time on the river, that would be easy to take care of; you could just take more launch trips (just money, no arranging necessary). If you wanted to take a boat down river towards Lake Albert (probably one of the best places to try to see the shoebill stork), you would need to arrange and pay for your own private boat trip which is also possible, but more pricey. If you wanted to take more game drives or go back to the base of the falls, you would probably need to do so through the Nile Safari camp or Paraa Safari Lodge, both of which are more upscale/expensive places. From the Red Chili restcamp, it would be easier to start with Paraa Lodge as it is closer (just across the river) and is within walking distance - though there can be large wild animals between the river and Paraa not to mention babboons.
- Determine how you would get back to Masindi/Kampala. You would probably have to wait until some tourist or tour group showed up with space in their vehicle. There really is no public transportation in the park, it starts again in Masindi. From Masindi, you could go back towards Kampala or head towards Hoima/Fort Portal, etc.
Now, if you are interested in poking around north of the Nile in Arua, Gulu, Kitgum, etc., as the answers have suggested, then I would probably take the Red Chili vehicle back towards Kampala and have them drop you on the main highway as they turn right to go towards Kampala and wait there for a bus headed towards Karuma. The buses from Kampala to all of those towns pass by there.