Revelations that the Millennium Tower in downtown San Francisco has sunk 16 inches and is tilting are just the opening act in a mega-million-dollar “who knew what and when” drama that portends even more troubles ahead for the high-end high-rise.

A geotechnical engineer hired by the 58-story condo tower’s homeowners association — and paid for by the developer — warned residents in May that the building is still sinking at a rate of about an inch a year and shows no signs of slowing down, according to those in attendance.

Patrick Shires, owner of a Los Gatos engineering company and a 40-year veteran in the field, said that over time the tower “most likely” will sink an additional 8 to 15 inches into the landfill beneath it at 301 Mission St. unless steps are taken to stop it. That means the worst-case scenario would have the South of Market landmark descending a total of 31 inches.

The building’s 2-inch tilt to the northwest at its base could get worse as well, Shires told the condo owners — some of whom are already taking legal steps to make someone pay for what they fear will be sinking home values.

Shires did not return our calls, and Charlie Goodyear, a spokesman for the homeowners association, declined to comment on the May session, except to say “it was conducted privately for the benefit of members.” He added that “the association has been assured that the building remains structurally sound.”

Millennium Partners, which opened the $350 million haven for the well-heeled in 2009, didn’t directly address Shires’ findings. Through spokesman P.J. Johnston, the company said it will work with residents “to monitor the situation and take further steps, should they be deemed necessary.”

One concern is earthquakes, which Stanford structural engineer Gregory Deierlein told us “may further aggravate the settlement in ways we don’t have much experience with.“

Some of the residents are pretty unhappy.

“The real issue for me is that it (the sinking) hasn’t slowed down,” said Jerry Dodson, a patent lawyer who lives with his wife, Pat, in a two-bedroom unit on the 42nd floor.

Their unit has no visible damage, but cracks and some water intrusion have appeared in the underground garage.

There has also been some cracking and buckling in the sidewalks outside the 419-unit building.

The Dodsons lay the blame on Millennium Partners for what they say is a flawed design, starting with the decision to anchor the structure with piles that go down roughly 80 feet into landfill rather than 200 feet to bedrock.

Millennium Partners has said the design is safe and is no different from what some other high-rise builders have done on landfill.

It has blamed the problems on a huge hole that was dug next door starting in 2010 for the still-under-construction Transbay Transit Center bus and rail terminal. That project is run by the Transbay Joint Powers Authority, which consists of San Francisco, AC Transit, Caltrans and the operators of Caltrain — meaning that if Millennium Partners’ assessment is correct, those taxpayer-funded government entities could be on the hook for tens of millions in repairs.

The authority has denied responsibility for “the tilt and excessive settlement” and, like the Dodsons, has blamed design flaws in the building.

That stance has Millennium Partners shooting back, accusing the transit center authority of making “misleading and self-serving” claims.

According to Johnston, the transit center authority knew the building was sinking faster after it began digging, but didn’t stop “despite this awareness, and assurances that it would suspend construction on its project if any impacts arose.”

We’ve confirmed that some owners in the Millennium Tower have filed legal claims against the authority, alleging that the problems are hurting their condos’ value. The claims, which the authority has rejected, are the first step in potential lawsuits.

The transit center authority, which spent $58 million to shore up the building before undertaking its big dig in 2010, said in a statement late Friday that the legal claims are “misplaced.” The statement also said the authority put the developer on notice more than two years ago that its building is flawed.

And by the way, the authority said, its consultant found last month that the building’s tilt at the base isn’t 2 inches — it’s more than 6 inches.

That wasn’t the only alarming news about the tilt. Shires, the geotechnical engineer, estimated that the lean at the base translates into an alarming 15 inches at the top of the building.

Millennium Partners’ Johnston took issue with both assertions. “We have every reason to believe there is no tilt or negligible tilt at the top,” he said.

As for the ground level, “my understanding is that it is less than 2 inches,” Johnston said. “We will be measuring all these issues in the coming weeks, and we will take appropriate steps when we have data.”

Residents aren’t angry just with the transit center builders. Some think the building’s owners owed it to them to tell them about the sink and the lean sooner than they did.

They say Millennium Partners first alerted representatives of the homeowners association to a potential problem in June 2015 — six years after the building opened and well after most of the units were sold.

But Millennium Partners said the sinking didn’t pose a problem early on. According to spokesman Johnston, “all closings of condominium units occurred before (the transit center authority) started major excavation.“

The developer originally estimated that the building would settle up to 6 inches over its lifetime. But geotechnical records show that by the time the transit center excavation began in 2010, the Millennium had already settled 10 inches. Millennium Partners then revised its estimates for the expected settling to between 10.3 inches and 12.3 inches.

The Dodsons, who bought their condo in April 2009, say no one told them about the sinking — or a 2008 agreement between Millennium Partners and the transit center authority to monitor how the excavation could affect the tower.

They say they and many of their neighbors found out about the problems only in May. Now the Dodsons are preparing a legal claim of their own — against Millennium Partners.

With everyone lawyering up, San Francisco Supervisor Aaron Peskin is trying to keep the legal dogs at bay. He’s planning to introduce a resolution this week “that makes it abundantly clear that regardless of the outcomes ... the city and county of San Francisco is not going to bail anyone out or pay one penny, because it’s not our problem.”

That may be wishful thinking. The city holds three of the five seats on the Transbay Joint Powers Authority board, and it recently took over construction management of the $2.4 billion transit hub after agreeing to provide a $260 million bailout loan.

San Francisco Chronicle columnists Phillip Matier and Andrew Ross appear Sundays, Mondays and Wednesdays. Matier can be seen on the KPIX-TV morning and evening news. He can also be heard on KCBS radio Monday through Friday at 7:50 a.m. and 5:50 p.m. Got a tip? Call (415) 777-8815, or email matierandross@sfchronicle.com. Twitter: @matierandross