In the first two weeks you should avoid strenuous exercise, and while on SS you should not really gdo anything strenuous that your body wasn't used to before you started. So if you were doing that kind of thing before, then after week 2, go for it. But if you weren't - don't. If you weren't doing exercise before then a gradual increase in activity is a good idea - increasing length walks etc - but nothing sudden or strenuous.
Lots of people have found that in weeks where they've done more exercise than their body is used to, they've had lower losses, gains, and or STS.
What happens is similar to when you asked about having two shakes to lose weight faster. On ss you're on 450-500 kcals / day, assuming your normal activity levels, your body can cope with that. If you suddenly start making big demands of those calories to fuel exercise, the body won't have enough left over. although fat burning in ketosis keeps us alive, our bodies (especially our brains) do need some calories from actual food (the packs). If it doesn't get all those easily accessible calories from the packs, because they're suddenly being burned up by exercise, it will start shutting down non essential functions such as hair growth.
Basically, the absolute fastest you can lose weight is by SS-ing. An average of 3.5-4lbs a week, if you are a woman. That's about as fast as people lose it after a gastric band, and about as fast as test subjects in clinical trials where they were given no calories at all. If you are 100% on SS and drinking between 2.25-4 litres of plain water a day, you are doing all you can.