There are 4 languages in Switzerland.
Most Swiss speak one and some even two of these languages more or less well.
Very few can speak all four.
65% of the Swiss speak German
22% of the Swiss speak French
8% of the Swiss speak Italian
0.7% of the Swiss speak Rätoromanisch
Your idea that it is not uncommon for people to speak 4-6 languages seems not really realistic.
These informations fit very well with my experience when living in Switzerland.
For me speaking a language means be able to converse with people in their language and not just to order dumplings in a restaurant.