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Top Democrats in both branches of the state legislature are now in agreement on a plan that would carve out hundreds of millions of dollars for one-time safety funding for the MBTA and $250 million to put towards a passenger rail expansion in western Massachusetts.

The Senate on Thursday teed up its version of a nearly $10.4 billion infrastructure bond bill (S.2989) that, like the legislation the House unanimously approved last month (H.4897), would create a $400 million pot that the T could tap as the transit agency works to address critical problems uncovered by a blistering federal safety investigation, according to a bill summary.

The redraft also mirrors the House’s $250 million in bonds toward the long-sought East-West Rail project and creates a commission to investigate whether Massachusetts needs a new public agency to build the project and then operate a western rail segment.

Beacon Hill Democrats effectively snubbed both Republican Gov. Charlie Baker and Springfield Congressman Richie Neal, who as chair of the U.S. House Ways and Means Committee is one of the most powerful lawmakers in Washington, D.C., by punting questions about control of the passenger rail expansion to a study.

Baker and Neal announced in April they had agreed to a path forward for the rail project, and said it would hinge on creating a new authority to oversee the service. The MBTA’s current commuter rail network stretches as far west as Worcester.

The Senate Ways and Means Committee bill set for debate Thursday has a bottom line more than half a billion dollars lower than the nearly $11 billion version the House approved, but senators are likely to amend the bill with earmarks for district projects.