BlackRock Inc. wants Congress to change an aspect of the Volcker Rule that is causing headaches within its hedge fund business. Billionaire Paul Singer wants risky derivative bets curtailed and says regulators should lose their authority to step in when large banks are failing. Uber Technologies Inc. says Washington should eliminate red tape that makes it difficult for the private ride-hailing company to issue shares to its drivers.

These are just a few of the wish-list items that corporations, banking trade groups and consumer advocates have submitted to Congress as the Senate considers overhauling financial rules. Mike Crapo, the Republican chairman of the Banking Committee, and Sherrod Brown, the panel’s top Democrat, began taking suggestions earlier this year as they work to craft legislation that spurs economic growth.