When you publish a book using variants, the publishing filter allows you to select one value for each variant criteria, whether you use single select or multi select variants.
If I am using multi select variants why can I only select one value from the criteria group when I am publishing?
When you create a variant, you can use the multi select option so you can assign all applicable values to a variant object.
If you have one variant topic that several values can use, you assign all of those values to that variant object.
For example, you have a product guide that includes a variant topic that can be used in guides for California or New York or Nevada. However, when you are publishing your book you are creating the published output for a specific variation of your content - this means you can only select one value for each variant criteria.
If you want to publish the guide for the latest product release in California, you select the book and the output type. Then in the publishing filter, you select the value for California. When the publishing job finishes, you have the latest guide for your California release.