They told me that they consulted with two "inmigration agencies" (I did not even knew that there existed such a thing), I would guess that they are experts in t

They told me that they consulted with two "inmigration agencies" (I did not even knew that there existed such a thing), I would guess that they are experts in these issues. My main weak point of entry is that I was applying to a consulting job in Data Science, and as such, it is not really possible to argue that there is no-one else left in the EU to take the job. Having a degree from the ETH indeed helps, but it wasn't enough. They have enforced quotas per canton, which means that once filled, no-one else is getting in. Furthermore, Swiss bureacracy is the most strict one I have seen in my life, so there is no much wiggle room to bend the rules.