It really depends on your body.
Even Dr. Atkins wrote that in the book. The two examples he gave were of a woman with a high metabolic resistance to weight loss and a man with a moderate metabolic resistance to weight loss. The woman stayed on Induction for the majority of her weight loss. The man moved to OWL Phase and proceeded through the Diet.
Dr. Atkins wrote in the book that the only people who could benefit from an extended Induction phase were those people with a high metabolic resistance to weight loss because staying on Induction might correct the metabolic imbalances that inhibit the weight loss. So the question is what is your metabolic resistance to weight loss and how do you find it?
Dr. Atkins wrote that at the end of your 14 Day Induction, you weigh yourself and look up your weight loss in the charts in the book. The problem I see frequently here is that no one bothers to do that. So we have folks who've "only" lost 9 pounds during the first 14 Days, mistakenly believe they have a high metabolic resistance to weight loss and mistakenly believe they "have" to stay on Induction to lose weight. If they had only bothered to take 2 minutes of their time to look up their loss in the charts, they would have seen that they have a moderate to low metabolic resistance to weight loss----like the vast majority of us do----and they wouldn't condemn themselves to staying on Induction. No, they would move to OWL Phase, eat a higher amount of carbs, eat a wider variety of foods and still lose weight. But since they don't bother to look things up, they remain on Induction unnecessarily.
Dr. Atkins spelled it out in the book that we, each, have a specific "critical carbohydrate losing level". That is each of us can eat a certain number of carbs and still lose weight. Only a small proportion of us will have to eat at Induction level carbs in order to lose weight. The vast majority of us can eat above it and lose weight. My CCLL was 50 net carbs daily----that's alot of food. We've had some members here who were eating over 100 net carbs daily and still losing weight. In my time here, there have only been about 5 people whose CCLL was 20 net carbs and the majority of them had medical issues that slowed their weight loss.
So unless you are one of those few people with a high metabolic resistance to weight loss, staying on Induction longer than the initial 14 days does nothing for you in terms of consistent weight loss, rapid weight loss, continued weight loss, etc. Over the years, we've noticed on ADBB that the people with average to low metabolic resistance actually hit a weight loss plateau if they stay on Induction too long. And by that time, they are too scared of carbs and too discouraged by their stall on extended Induction that they are absolutely terrified of adding 5 net carbs of veggies to their menues.
But the choice is yours.