In certain cases, certain legally regulated exceptions from the admission requirements are possible. The following overview is not exhaustive, but represents the most frequent cases:
Management or specialist transfers in international companies
The precedence rules do not apply to operational transfers for senior managers and essential specialists in international companies.
Some international non-government organisations have arrangements with Berne. IATA is one. Their permits for non-EU nationals, for example, are not subject to the Cantonal quotas. There aren’t very many though.
Typically it means inter-corporate transfers are not or less subject to permit quotas, but you will have to be at a specialist or senior level, and probably have to have worked for the company for a while first. But inter-corporate transfers are definitely one of the easiest ways for non-EU people to move to Switzerland.