When you filter a book in Author you can only select one value for each variant criteria, whether you have used single select or multi select variants.
You can select only one value for filtering even if you use multi select variants
When you create a variant, you can use the multi select option to assign all applicable values to the variant object. So if you have a variant topic that can be used by several values, you would assign all of those values to the variant object. For example, the topic can be used by California or New York or Nevada. However, when you are filtering, you want to see the content that is relevant to a specific value. This means that you can select only one value for each variant criteria.
Anne Ortha has created one variant topic for the X1000 Acme teleporter with specification details relevant to both California and New York. In her teleporter guide, she also has several other topics that have variants only for California, variants only for New York, and variants only for Nevada.
Today Anne wants to make updates to the guide for the latest product release in California. To do this, she opens the book and updates the filter by selecting the value for California. The book content is updated to include the content that is relevant to California (that is, the single and multi select variants that have the criteria value for California assigned).