In a one aircraft, non-public transport operation it makes no difference whether you call yourself Captain, Co-Captain or F/O. These titles only have any true relevance where they can be quantified by an identifiable command structure outlined in the AOC and approved by the relevant authority. In my opinion, if the new title entails more responsibility then in an ideal World it should pay more. However, in these uncertain times you might just have to take a view on that.