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?

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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

WindowsServer2016LicensingFAQ_as is 2016-09-08

WindowsServer2016LicensingFAQ_as-is-2016-09-08Download
WindowsServer2016LicensingDatasheet_as-is-2016-09-08Download