I think the rules doesn't allow this sort of move:
Reminder: to make a bridge, you must jump
onto other pieces. This means that you can only
do it with a piece that is already on the board. Its
PÜNCT must always be moved in a straight line
and be placed on one of your own pieces!
The PÜNCT of the piece must be placed on one of your pieces, not over it.
This reading of the rules would limit each player to 8 pieces that can bridge: the 4 straight pieces with the punct on the end (the E pieces), and the 4 angular pieces with the punct on the end (the 2 L pieces and the 2 R pieces).