Given the issues of finishing 3 and 4 part chains I believe a solution could be allowing...
3 part chain; allow going from first to third as option, this does not mean you cannot try for all three parts
4 part chain; allow going from first to third and then on to fourth, or from first to second to fourth. Again if you want to try for all four parts have at it
3 part chain; allow going from first to third as option, this does not mean you cannot try for all three parts
4 part chain; allow going from first to third and then on to fourth, or from first to second to fourth. Again if you want to try for all four parts have at it