But e-mails obtained by the Globe show that Brown’s work on behalf of the financial sector did not stop when the law was passed. In the second stage, as regulators began the less publicly scrutinized task of writing rules amid heavy pressure from the banking sector, Brown urged the regulators to interpret the 3 percent rule broadly and to offer banks some leeway to invest in hedge funds and private equity funds.

Supporters as well as critics of the banking industry agree that Brown’s suggestions would mean looser regulations for banks, though specialists disagree on the extent of the impact.

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Ann Graham, a lawyer formerly with the Federal Deposit Insurance Corp. and an advocate of strict regulation who teaches banking law at Hamline University in Minnesota, said Hoopes’s memo urges regulators to “substantially undercut the Volcker rule’’ in ways that would allow banks to skirt the 3 percent limit on hedge fund ownership and delve into riskier investments.

Hoopes’s memo lays out seven areas of the rule that Brown wishes to shape.