Switzerland has previously participated in Erasmus, which was set up in the 1980s to facilitate student exchange between European countries.
But following the country's anti-immigration referendum in 2014, which approved the principle of quotas on immigration, the EU suspended Switzerland's membership of Erasmus+ (the scheme's 2014-2020 incarnation), saying the country's stance was no longer compatible with the programme, which depends on the principle of free movement of people.
Later that year Switzerland announced an interim solution allowing it to offer student exchange as an Erasmus+ ‘partner country' rather than a full member, by arranging a series of bilateral agreements with individual European universities under the new Swiss-European Mobility Programme (SEMP) banner.
As it no longer receives funding from Brussels, Switzerland must fund the scheme itself, supporting both Swiss students who wish to study in another country and foreign students who want to come to Switzerland – a requirement if Switzerland wants its own students to be able to study elsewhere.
In 2016 the federal government allocated 25.1 million francs ($25.6 million) to the task, funding a record 10,781 Swiss students and foreigners on study and vocational training placements, said Foundation ch, which is currently charged with running the SEMP scheme in Switzerland.
That's a 12 percent increase on last year's 9,650 students, funded by a budget of 23.9 million francs.
8,650 of this year's exchanges are at tertiary level, up from 7,874 in 2015, an increase “principally explained by a more generous budget this year,” said the foundation.
Among 2016's cohort, 4,789 Swiss students travelled to higher education institutions elsewhere and 3,861 came to Switzerland.
The success of Switzerland's new study abroad arrangements will be of interest to Britain, whose future in Erasmus has also been thrown into question since it voted to leave the EU in June.
As for Switzerland, it has until February 2017 to find a way of implementing quotas on immigration without upsetting its relationship with the EU.
Should a bilateral solution be found that satisfies both parties, it's possible that Switzerland's membership of Erasmus+ may be reinstated.
A newly established Swiss government body, the Swiss Foundation for the Promotion of Exchange and Mobility (SFAM) will take over running SEMP from January 1st 2017.