The language I've seen for the rule is increase 10% of local market rates, not the base rate of the house itself. So your neighbors rent would increase by more than %10 of their base.
An older, existing rule regulates in what way you can increase the rent for existing tenants based on the rent they currently pay. (You mostly cannot unless you modernize the building.)
This new rule states that you cannot set the rent above 10% of the local market average for any tenant.
So for existing tenants, most likely the first rule applies (because new tenants rise the average), for new tenants the second applies.
Or did I miss something?