This might be a wording issue. If you start with the primary option (1 out of N, so radio button) you can then present an "additional options" list where it's legal to choose 0 additional options (so checkboxes make sense).
This makes additional sense because "primary" is semantically related to "first", so it's natural to start the dialog with "the primary option". As there's no ranking of additional options, we don't have a "secondary option" - they all are "additional options". We use words in the order that people expect to see them. This decreases the cognitive load.