Not if you are following the Ideal Protein plan, and expecting typical Ideal Protein results. You cannot lose 2-4 pounds per week on many other diet plans. or just with diet and exercise.
IP is a ketogenic diet - what that means is that your carb intake is so low that you deplete your glycogen stores (which your body normally uses for energy) and instead of burning glycogen your body starts burning fat for energy (known as ketosis). When you add in carbs that are not on plan, you are pushing yourself back into the zone where your body is not in ketosis and not burning your fat stores for energy.
The IP program is ALSO designed to be low enough calorie (and remember that grains, high carb veg and fruits are ALSO higher in calories than the veggies allowed on plan) so that there is a big deficit between what your body needs to function, and what you are taking in. That's what produces the high losses when compared with other diet plans.
There are diet plans with a similar structure to what you are proposing. If you don't feel that you would be a good fit for the IP plan as it is written, you may want to investigate those options. The 5:2 diet plan is one of those, and might be better suited to your needs:
http://thefastdiet.co.uk/