Create a table style based on an existing table?

Using Word 2016. I've got a standard format that we use almost exclusively in our reports that are generated using a tool that outputs a standard .docx file that gets its style information from an imported template. I've been able to get the formatting perfect in most of the document by updating the Normal style to match a correctly-formatted selection.

Is there a way to do this for table styles? I've saved the format to the Quick Tables gallery, but I am not sure that that would be enough as the style information is applied automatically.