You'd probably be better off dividing the base/parallel slots by boxes.
1. Base slot boxes 1-6
2. Base slot boxes 7-12
3. Parallel slot boxes 1-6
4. Parallel slot boxes 7-12
Or you could do 8 slots: base/parallel boxes 1-3, 4-6, 7-9, 10-12.
Of course slot prices will increase but there would be no dispute as to which player belongs to what teams.
I'm in for 1 if this generates interest.
Collecting: Ryan Tannehill