Officials said 11 men and nine women were killed, most from Switzerland but also a couple and their son from Austria.
The company JU-AIR had bought three of the vintage Junkers propeller aircraft, which are known affectionately in German as "Auntie Ju" planes.
Officials said Sunday they weren't aware of any distress call made from the plane, adding that the investigation into the crash is expected to be "relatively complex" - though there's no indication of foul play.
Daniel Knecht of the Swiss Transportation Safety Investigation Board told Blick in a news conference that the vintage aircraft may have hit the ground near-vertically at a high rate of speed.
The crash happened hours after a family of four were killed when their small plane went down further west in the Swiss Alps.
Knech also ruled out the idea that the plane had hit an object, such as a cable or another aircraft.
Authorities are investigating what caused the deadly crash.
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Police in southeastern Graubuenden canton (state) said a several-seater plane crashed Saturday on the Piz Segnas mountain striking the mountain's western flank about 2,540 meters above sea level.
The area around the crash site, which is popular with hikers and skiers and includes a glacier, was closed to the public.
They were produced in Germany between 1932 and 1952, serving both as passenger and military planes.
The company's flight operations were suspended, it said.
Each of the pilots flying it had over 30 years of experience in both the military and civilian sector. He said it had its full annual service during the winter, and "we know of no technical problems with this aircraft". The plane holds 17 passengers, two pilots and a flight attendant.
A brochure on the company's website listed the cost of the 2-day Locarno trip as 1,130 francs ($1,136), including meals and a night in a hotel.