very simply: if corporations are people, then people must be corporations. Which means people should be able to avail themselves of all the juicy corporate-welfare tax breaks given to corporate legal entities.
It's pretty easy to follow this train of thought down some very interesting tracks. We'd start by allowing individuals to only be taxed on their profits instead of their income, personally.
http://www.washingtonpost.com/opinions/catherine-rampell-people-should-claim-the-same-rights-as-companies/2014/07/24/460aea0c-135b-11e4-9285-4243a40ddc97_story.html