No, this is not a project to abolish corporations. The only thing this project is proposing is to end the inappropriate benefits offered by the legal fiction of "corporate personhood" that gives the artificial entity called a corporation the status of a living, breathing human being, and as such acquired "human rights protections". This legal fiction is the what gives corporations equal access to government, the right to lobby (freedom of speech) and all other protections and rights offered by the Constitution to any other human being. This single legal contrivance lies at the heart of why corporations have been allowed to get away with what they have been getting away with.
The fact of the matter is the vast majority of corporations don't have any need to exploit this loophole and don't. It's primarily the huge multi-national corporations that do and reek the most havoc because of it.
So when we are successful at ending this ridiculous notion that corporations are people, nothing else about corporations will change. They will not all be shut down. They will just be subject to the will of the people to a far greater degree. And they will no longer be able to write all the legislation they wish to make every rotten thing they want to do legal. And they won't be able to give ANY money to politicians or interfere in the election process. And they won't be allowed to tie issues up in court forever while they continue to rape and pillage to their heart's content.