We are thinking about doing a trip from Amsterdam to Basil and taking a seven day break to tour Switzerland then get back on the river and continue to Budapest. Anyone ever done it? And how do you get from Basil to Passau to catch a seven day cruise to Budapest?
Possibly, but most people would just do the Amsterdam to Budapest cruise, with a land stay at the beginning and/or end.
First, thoroughly inform yourself with the possible drawbacks of a river cruise. Water levels are one important factor that can turn your river cruise into a bus tour for all or part of the itinerary if the levels are too high or too low. Both the Rhine and Danube have experienced historic low levels this year that have resulted in this for many if not most cruises there this summer. This is a known risk, and is included in the T&Cs of every river cruise line contract.
Getting from Basel to Passsau would require either an all day trip by multiple trains, or a somewhat shorter trip flying from Basel to Munich, a train to Landshut, and then a bus to Passau.