Three scenarios being discussed by the WH and Hill Democrats:
Go back into the law and ban expenditures from corporations based on fact that they retain lobbyists or have contracts with governments. The Court would probably reject this, but Dems could pass it and the president could sign it. A modest political victory with no real effect.
Another avenue would be to impose a requirement that shareholders have to approve of expenditures from a corporation's general treasury. This might serve as a deterrent. I don't know whether this proposal would get 60 votes, nor do I know whether it would sustain a legal challenge.
A third idea: make the "Stand by Your Ad" requirement apply to all campaign ads. The head of an insurance company would be forced to say, "I'm Honus Wagner, the CEO of Acme, and I stand by this ad." This can pass Congress and will pass muster with the courts. The hope is that it would deter corporations by subjecting them to scrutiny they do not want.
And then -- new disclosure laws. Which don't have much of a deterrent effect.
Undoing the soft money ban would help parties and candidates -- the major losers here - but there is no appetite for that, and it would completely undercut the rationale for campaign finance reform in general.