I applied for a Schengen Visa to Switzerland while I had a valid one for Germany till 3rd Sep 2016 (I have already traveled to Germany on this visa). The visa was granted, however from 4th Sep 2016. I am due to travel for a 2 week business trip to Switzerland from 29th Aug 2016. Can I travel with the two above mentioned visas? Germany one for the 1st week and Swiss one for the next week? The Germany visa was stamped on my old passport which has since been cancelled and new one issued due to expiry date. Is the Germany visa still a valid one though on the old passport?
There are several aspects to the question. The Swiss consulate did the recommended thing and you can certainly use your German visa for the first part of the trip, as long as it is a multiple-entry visa and there is no gap between your two visas. We already have a few questions on this, e.g. Traveling on back-to-back Schengen visas
An additional complication in your case is that your old visa is in a cancelled passport but that's OK too. I am not able to find a reference right now but there was even a court case about this (I mentioned it in a comment to some earlier question I think). What you need is (1) a valid passport and (2) a valid visa, not a valid visa in a valid passport.