lukebianco yes there is.
From Windows 8 forward, Microsoft has a feature called Branch Office Direct Printing. Here are the technical details.
This is ONLY a Windows solution so if you have Macs printing, they will send the job the whole route.
The logging of the job will be copied to the Windows PrintService / Operational logs on the print server even though the printing never goes through the server.
The status of the patent on the feature is listed as abandon. https://patents.google.com/patent/US20120127512A1/en but let me know if you have questions since I am listed as one of the inventors.
Make sure you are using a Standard TCP/IP port on the print server and that you are not blocking print jobs if they do not originate from the print server.
Enable the feature using your favorite tool for managing Print Servers Print Management Console and you can set the rendering mode using PowerShell as well.