I would stick to one plan only personally. I'm a huge fan of SW, but I've never heard of the alkaline diet so wouldn't know how it would match across to SW.
You can lose plenty of weight on SW (as much as you need to) if you stick to it. One family lost 20+ stone between 4 of them (I think! May have been 5 people)
SW is great in my opinion because it's a healthy eating plan more than a diet. You can still eat 'bad' things, you just need to count them in your Syns allowance.
Plus you still get some of each food group (fruit/veg, protein, carbs, dairy, fibre) so you aren't cutting anything out.
Reading what I could find on the Internet, the alkaline diet asks you to cut out Dairy, eggs, meat, most grains and processed foods. Basically an almost vegan diet.
You can be vegan and still do SW, there are plenty of people who do.
Obviously it's your decision which one you follow, or if you combine them. But for me, I'd have to chose one and as I am a meat eater and will not cut that out, SW is my way forward
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