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Senate President Stanley C. Rosenberg is open to the House version of a controversial transgender antidiscrimination bill, another sign the legislation is likely to become law before Beacon Hill’s denizens begin their summer recess in August.

“It doesn’t fundamentally undercut the purpose and the principles of the bill,” Rosenberg said this week. He said the extra provisions in the House bill do no harm, but he also called them unnecessary.

Governor Charlie Baker has expressed a broadly positive take on the House bill, and Attorney General Maura Healey supports it.

The bill, set for Senate passage Thursday, would protect transgender people from discrimination in sports arenas, restaurants, movie theaters, malls, and other public accommodations. It would allow people to use the restrooms and locker rooms that match their gender identity.

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The House rewrite, among other differences with the Senate version, would empower the attorney general to issue guidance on when or how legal action may be taken against people who assert gender identity for “an improper purpose.”

That’s partly to address worries from opponents who claim that male sexual predators, under the guise of being transgender, could enter women’s restrooms and locker rooms. Proponents of the bill say those worries are unfounded.

The addition is also seen as a way to make it easier for moderate Democrats in the House — worried about reelection — to vote for the bill.

On Tuesday, Rosenberg, a longtime supporter of transgender rights, said there does not seem to be a lot of support for the House version among senators. He said the additional language is redundant.

“Our analysis, based on the information from our legal team, is that it does no harm, and it’s unnecessary,” he said. “Because if people behaved in the way that the language seeks to avoid, there are already statutes . . . that would declare certain of those actions as illegal, and they would be subject to arrest and prosecution.”

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But, he indicated, most important is getting the bill into law. “As long as eliminating discrimination is still the heart of the bill, then the bill works, if it gets signed into law,” he said.

The comments from the Senate president mark the latest in the careful public dance between him, Baker, and House Speaker Robert A. DeLeo, who supports passage of the bill.

Baker, a Republican who opposed such a transgender public accommodations effort during his failed 2010 run for office, has taken heat for avoiding a position on the issue in recent months. While he has repeated the refrain that he doesn’t think anyone should be discriminated against, he’s dodged taking a stance on the legislation.

But in late April a Baker spokesman said the governor “appreciates the added clarity that the House’s revisions provide into how the provision would be implemented across the Commonwealth.”

The House is anticipated to vote on the bill after it passes the Senate. If, as expected, the House and Senate versions differ, each chamber could appoint members to a conference committee. Or one of the chambers could accept the other’s version.

Baker could sign a bill into law, allow it to become law without his signature, veto it, or send it back to the Legislature with a recommended change.

A recent Suffolk University/Boston Globe poll found more than half of likely voters support the transgender public accomodations push.

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Joshua Miller can be reached at joshua.miller@globe.com. Follow him on Twitter @jm_bos. Click here to subscribe to his weekday e-mail update on politics.