There isn't a check on the checkboxes at this time to control how many are selected at one time in order to add to cart ...

I am currently debating this feature and where it is best to store the data ...

If this is stored in the products_attributes table and assumes if you set it to 4 meaning minimum of 4 checkboxes and you have 12 checkboxes but only have this setting on 10 of them because you forgot it on 2 of them ...

then takes the highest number found of the 12 attributes for how many checkboxes are required as the correct value ... would this work?

I think, in theory, that would provide the most flexibility ...

This way I can have an Option Name:
Pizza Meat Toppings

Option Values:
Pepperoni
Ham
Chicken

And in those would be a minimum 1 setting ...

Or Pick 3 colors and give a list of 12 checkboxes where the minimum on each of the attributes is 3 ... and even if I forget to mark 2 or 3 of these with the minimum setting, because I managed to get at least 1 of them marked with a minimum setting and the same for a maximum setting ... this should work ...

Now to just get it all working happily together and not break anything ...