this is not a parasite cleanse, although some people do release parasites on the cleanse. you can combine the mc with parasite cleanse and pb shakes, this is called the ultimate cleanse- this is what i did for my first fast, i think it is more focused on the bowel than the lemonade only fast.
i know clark emphasises doing parasite cleanse before liver, but some do Liver Flush without having done the parasite cleanse.
my inexpert recommendation would be to do the parasite cleanse together with pb shakes after you come off the mc, while eating healthy, do the liver cleanse after you finish the parasite cleanse, and continue with the pb shakes after your liver cleanse

you might get better answers in the liver cleanse forum

i'm on day 26 of Master-Cleanse and have been doing a parasite/worm cleanse since Day 6. I went to the health store looking for Wormwood , clve and green Black-Walnut hull---Clark's prescription. The clerk at the health food store asked "Do you want the 'Worm parasite Cleanse'. It has all three of her ingredients, it was less than $15 (clark's is $45) and it worked. By day 8 I was visibly passing clear, 1/2" worms. I added a dropper full into my limeade four or five times a day. I've continued it daily (i'm on my 2nd bottle) to make sure I zap all invisble paraites. The product I bought is by Quantum Health. Good luck. I plan to do the Liver Flush after my 40 days.