State lawmakers appear headed for an unusually complex and volatile finale to their two-year session, with legislation affecting energy policy, veterans’ benefits, transgender rights, and the ride-hailing industry hanging in the balance — on top of a deeply unbalanced budget.

With less than six weeks until the legislative season ends, the traditional chessboard of Beacon Hill priorities is more crowded than usual. And it is imbued with increased sniping between the House and Senate and tension created by a federal investigation of state Senator Brian Joyce, a Milton Democrat. Further complicating the showdown is Senate President Stanley C. Rosenberg’s drive for “collaborative leadership’’ in his chamber, which will face its stiffest test yet.

Among the measures still pending are a bill that would expand transgender rights in public places, including bathrooms; legislation that would regulate ride-for-hire firms such as Uber and Lyft under tighter state supervision; and a heavily lobbied bill designed to diversify the state’s energy sources. All of them could be ensnared in multidimensional negotiations.

“I can’t remember a time that I’ve served that this many big things are still up for grabs,’’ said state Senator Benjamin Downing, a five-term Pittsfield Democrat who cochairs the telecommunications, utilities, and energy committee.

The clogged schedule follows nearly two years that have seen little progress on a host of issues. Now, due to the sheer number of pending initiatives, even longtime legislative observers see extraordinary unpredictability about which will advance and in what form. Along with the policy measures, lawmakers are facing declining revenue estimates that will force heavy changes to the state’s operating budget.

“The give-and-take that normally characterizes the end of the session will be on steroids,’’ said Eileen McAnneny, president of the business-backed Massachusetts Taxpayers Foundation.

For instance, the House and Senate, both dominated by Democrats, are largely in agreement on the transgender rights bill, but they disagree over how quickly the changes should take effect and over language in the House version that would charge the attorney general with handling people who assert gender identity “for an improper purpose.’’

Rosenberg and others have called the language unnecessary because such instances would be covered by existing statute, but lawmakers acknowledge that the clause provided political cover for Governor Charlie Baker and House members on the fence about the bill to support it.

The Senate wants changes to go into effect immediately, and the House wants them to take hold in January. If the chambers cannot resolve their differences in informal negotiations, the bill would go to a conference committee, where it could be buffeted by deliberations over other, seemingly unrelated bills.

Representative Sarah Peake, a Provincetown Democrat and member of Speaker Robert DeLeo’s leadership team, scolded the Senate for what she said was throwing the bill into jeopardy. “I do not believe that this is the time to roll the dice with people’s civil rights,’’ she said.

But advocates and the Senate judiciary chairman, William Brownsberger, said they are confident the bill will reach the finish line. “I’m very hopeful that everything will get squared relatively quickly,’’ Brownsberger said last week.

“There is no doubt in my mind that we will see a bill within a month, at most,’’ Arline Isaacson, a longtime lobbyist and cochair of the Massachusetts Gay and Lesbian Political Caucus, said Wednesday.

The legislative calendar is further pinched by both national parties holding their conventions next month, which will draw lawmakers out of town. Legislative leaders have apprised members that they should expect unusual weekend sessions to compensate.

Meanwhile, Rosenberg has pursued a more wide open style of moving the Senate agenda, leading to lengthy deliberations among members that represent a break from previous regimes. That shift has created tensions with the House, a more top-down body. And House members are expressing frustration with his approach.

“The Senate’s paralyzed right now,’’ said another member of DeLeo’s leadership team, speaking anonymously to discuss interchamber relations. “We can’t get them to focus.’’

Senators rejected that view. Senator Dan Wolf, a Harwich Democrat and Rosenberg ally, said, “If anything, I feel the fierce urgency of the clock running, but I think there’s a really good process going on in both chambers.’’

House Democrats were irked earlier this month by Rosenberg’s address to the state party convention, which offered a compendium of Senate-passed measures that are stalled in the House.

Peake called the remarks “almost taunting,’’ adding, “That kind of grandstanding is just divisive.’’

But many senators privately blame the House for moving too slowly on bills the Senate has already passed, a long list that includes a major proposal to expand the number of charter schools in the state while imposing tighter operating restrictions; a comprehensive agriculture bill; gender pay equity legislation; and a measure that would increase the attorney general’s authority to represent workers in wage disputes.

“I think there might be more things in play because Stan wants to have more of an open way about it,’’ Downing said. “But I don’t think the logjam speaks to him.’’

Some of those measures have drawn strong opposition from the business lobby, which has come to view the House as the safer harbor, as Rosenberg and an increasingly liberal membership have helped pull the Senate left in the year and a half of his presidency.

For his part, Baker sounded an optimistic note that many of the major bills would reach his desk.

“If you look at all the stuff that’s teed up between what’s on the House side, what’s on the Senate side, and what’s in conference, I agree, there’s a lot of stuff there,’’ he told the Globe on Wednesday. “But I also believe that a lot of it, one way or another, is going to find its way through the process.’’

Jim O’Sullivan can be reached at jim.osullivan@globe.com.