We have purchased Windows Server 2016 Standard. By doubling (tripling, etc.) of the purchased licenses, is it possible to run 4 (6, etc.) virtual machines on one server, as it was the case with Windows Server before?

Yes, this is still possible. If there are more than two virtual instances of Windows Server 2016 Standard required, all physical cores on the server must be licensed again.

Source:

WindowsServer2016LicensingDatasheet_as is 2016-09-08