I don't think they need to be actively broken up by the government itself.
We simply need to raise capital requirements to have them be proportionately larger as a bank gets larger, i.e. bigger bank = bigger % reserves
Investors will realize that having a bank be too large reduces returns, and they will "release shareholder value" by splitting them up in ways that stand a good chance in succeeding.
A simple, easy to understand government rule, that lets private sector actors run the particulars.

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