If someone had a serious amount of weight to lose and had spent the requisite time teaching their body to burn fat, I would have them try 24-, 36-, and 48-hour fasts. Probably not much longer than that, but probably with some frequency (2 days every week or every 2 weeks, for 6 weeks, and then rest). As long as they were exercising and performing substantial movement throughout the day, they would be burning fat, utilizing ketones, and possibly even building muscle.