I'm only speaking from my own experience and I do realize that everyone is different......but when it came to the veggies in the lowest carb category (ie: spinach, broccoli, cauliflower, lettuce, cukes, celery, etc.), I never really worried about the amount I ate. And I ate LOTS (and still do).
What I worried about the most, in terms of amounts (of net carbs)...was cheese, cream cheese, etc.....and dairy (unless you are lactose-intolerant) does tend to be constipating anyway.
But the Atkins-friendly, induction-friendly items that prevent constipation...the hi-fiber, low-carb veggies and the water.....I had plenty of (and never measured) and they will definitely make up for the tendency of meat and dairy to be constipating.