Now, Public Citizen is arguing that Bank of America fits the bill — its assets equal about one-seventh of the nation's total economic output — and needs to be broken down.
The advocacy group also sent regulators a letter signed by several law professors asking for an investigation into the risks presented by Bank of America's current state, and how the financial system would handle its collapse.
The pressure comes as regulators continue to grapple with eliminating the "too big to fail" problem that gripped the financial system during the 2008 crisis, forcing the government to pump billions into ailing institutions that threatened the well being of the entire marketplace.
The law responding to that crisis, Dodd-Frank, hands regulators several new abilities to address this issue. Banking regulators now require large and significant institutions to provide blueprints for how they could be dissolved in an orderly fashion if they were to fail, and also must submit to regular stress tests on the stability of their holdings.
In addition, regulators now have the ability to deem certain institutions like large banks and other highly interconnected entities as "systemically important." That designation carries with it heightened regulatory requirements, as the government works to prevent those vital entities from going under.
Republicans critical of the new law have argued that such a designation actually formalizes the "too big to fail" designation for certain institutions. But its backers, including President Obama, have repeatedly maintained that the new law ensures that massive bailouts of the financial system will not occur again.
"You’re required to write out a 'living will' that details exactly how you’ll pay the bills if you fail — because the rest of us aren’t bailing you out ever again," Obama said during Tuesday's State of the Union address.