You have Atkins listed as your plan, so are you referring to his "Fat Fast"? If so, his guidelines were that it was only for those metabolically resistant. That would be by definition someone stuck on a plateau (halt in weight loss that lasts at least a month while following plan and nothing to do with changes in food intake or lifestyle).

If that is where one ends up, chapter 20 in DANDR, which covers metabolic resistance: causes and solutions, explains that one can do the fat fast for about a week and then move back into induction. Atkins also says it is actually dangerous for anyone who is not metabolically resistant. I would take that to mean it would not be a good idea to plan to cycle through that extreme of a cut in calories repeatedly without possible negative health results.

Hope this info helps, and if you are following a different plan now sorry if this doesn't apply.

Personal experience is that time, patience, and following your plan exactly as written can and does work with realistic expectations. Just like the turtle, slow and steady can win the race! Good luck