thanks for the response first! so you got the point that the major difference I would say between the shared host setup and the VPS setup is the use of the server engine, in the shared host they use the Apache while it the Nginx on the VPS. So if site migration succeeds between these two server engines on a single site setup, I don't see any reason why it won't work on multisite setup as well. Do you share the same opinion?
That said, the installation of Nginx with WordPress multisite setup needs Nginx Helper plugin, I still look for a good documentation on that installation though. I mean, Nginx + WordPress Multisite + subdirectory setup