Certainly it is wrong to be cruel to animals and the destruction of a whole species can be a great evil. The capacity for feelings of pleasure and pain and for the form of life of which animals are capable clearly impose duties of compassion and humanity in their case.

Ideal legislators do not vote their interests.

How did Madison get separation through Virginia and later Congress? The Baptists, the Presbyterians, and the smaller sects hated Jefferson; to them he was a secularist of the worst kind. But Madison could get Jefferson's bill passed because the Baptists, the Presbyterians, and smaller sects who were excluded in New England and in the South got together for their own protection.

You might say that, if citizens are acting for the right reasons in a constitutional regime, then regardless of their comprehensive doctrines they want every other citizen to have justice. So you might say they're all working together to do one thing, namely to make sure every citizen has justice. Now that's not the only interest they all have, but it's the single thing they're all trying to do. In my language, they've striving toward one single end, the end of justice for all citizens.

Ideally a just constitution would be a just procedure arranged to insure a just outcome.

A scheme is unjust when the higher expectations, one or more of them, are excessive. If these expectations were decreased, the situation of the less favored would be improved.

There are various ways you might define the common good, but that would be one way you could do it.