I’m trying to create a key to only affect the blog_public option. The key with the following parameters works, but also affects the other options on the page, like show_on_front, posts_per_page etc.
At the moment, there is option to make only one option in a form updated. However, there is a workaround that includes the Boilerplate extension tokens.
For example, all fields that have same value for each site leave as is, all options that have unique value on each site, manage via custom token.