There is no language where, given a constituent class including both topical and non-topical members, the verb would agree with some or all of the non-topical members but with none of the topical ones.
Standardized
Provided there is a constituent class including both topical and non-topical members: IF the verb agrees with some or all of its non-topical members, THEN the verb agrees with at least some of its topical members.