Hmm, I am not sure there is a way to limit how many items someone can assign themselves to but you can track how many they have assigned themselves to by: 1) the activity log, and 2) the workload widget.
I would suggest using the workload widget to see how close to capacity each person is with the items they’re assigning to themselves.
However, for limiting your team’s actions on a board, it might be worth setting board permissions or column permissions.
What do you think?