Beneath the shadows of the Colosseum in Rome, hard-hats and engineers are digging out space for the Italian capital’s newest metro stop.

Across the Alps in Paris, planners are building a new subway station near towering apartment blocks in a dense city neighborhood. 

And London has bored miles of tunnel at depths of more than 100 feet to construct a new express line through the heart of its financial district.

Yet these complicated projects in Europe’s biggest, densest and oldest cities are getting built for a fraction of what the Metropolitan Transportation Authority says it needs to extend the Second Avenue Subway to East Harlem, a Post investigation has found.

The MTA is digging the endless money pit with design decisions for building stations twice as big as necessary, the investigation showed.

MTA officials plan to spend $7 billion, a figure the federal government warns could grow to $7.7 billion. And that’s the stripped-down plan.

The three European capitals could build an apples-to-apples project for just $2-$2.3 billion — price tags The Post calculated to include worst-case engineering scenarios.

The MTA’s stratospheric spending leaves New York unable to afford major subway expansions, even as it drowns in traffic and struggles with some of the nation’s highest asthma rates.

It’s not for lack of resources. The MTA’s $55 billion budget for major projects and system upgrades could, for example, repair every unit of public housing in the Big Apple.

Yet the five boroughs have added just four new subway stops over the last 30 years as London and Paris officials raced ahead with projects to shorten commutes and reshape their cities.

On Second Avenue at 96th Street, where the Q train now ends and the posh environs of Yorkville give way to East Harlem, officials have promised to bring expand the subway there — where walk-ups, bodegas, churches and public housing towers line the street — for nearly 100 years.

Supporters say the extension is key to fixing the neighborhood’s entrenched poverty and chronic health problems linked to pollution.  

But the eye-watering price tag means the MTA can’t break ground until it scores $3.4 billion from the Biden administration.

“You simply can’t support the density of the region and an enormous part of our economy evaporates if we don’t have a functioning system — much less a superlative system,” said Robert Yaro, who was one of New York’s leading planners for two-plus decades as the head of the Regional Plan Association.

“We have to solve this problem because we have to build these projects,” he added. “The city — and region — is not going to succeed in the long run unless we can create new capacity in the system.”

Experts said The Post’s findings reveal the need for further reforms in how the MTA designs and builds, even after changes already spearheaded by its chairman, Janno Lieber.

Lieber led the World Trade Center reconstruction and was brought in to overhaul the MTA’s major projects arm after delays and overruns imperiled its $11 billion train hall beneath Grand Central for the Long Island Rail Road.

“The reforms the MTA has implemented now allow the MTA to do projects without putting the agency at existential risk,” said Alex Armlovich, who closely examined the MTA’s operations at the Citizens Budget Commission.

“The Janno turnaround stabilized the MTA at its current enormous costs,” he added. “The problem is they have not yet begun to get those costs under control.”

The Post interviewed more a dozen people and reviewed more than 1,000 pages of reports, schematics and financial audits to compare the East Harlem extension to projects in London, Paris and Rome.

The review shows the MTA is repeating a key design decision that propelled costs into the stratosphere for the first phase through the Upper East Side: Building stations twice as big as necessary.

Take the first of the three proposed new Q train stations: 106^th Street.

Every Q train is approximately 600 feet long. They arrive and depart from platforms that are just a tad longer, 615 feet.

But diagrams the MTA filed with the local community board show the agency plans to dig a station box — the structure that the stop, its platform and all its components fit into — that’s more than twice the size: some 1,400 feet long. It stretches all the way from 105th Street to north of 110th Street.

The boxes for the stations at 116^th Street and 125^th Street are also massive, the documents show, measuring in at roughly 1,300 feet and 1,200 feet respectively.

Oversizing the three stations at 72nd, 86th and 96th street was a key reason behind the Upper East Side extension’s record-setting price tag. Each stop cost $633-$794 million and has caverns of roughly 1,000 feet long or bigger.

“The bigger the hole, the more money you have to spend,” said Eric Goldwyn, a researcher at New York University who led an exhaustive 424-page report that revealed how the MTA oversized the Upper East Side stations. “It’s expensive and disruptive. You try and optimize those things as much as possible.”

It stands in stark contrast to how London, Paris and Rome design stations, which carry price tags that are a fraction of the MTA spent.

Over there, designers keep the station boxes roughly the same length as the train platforms to minimize costly digging and neighborhood disruptions.

Officials in Paris squeezed a 410-foot platform in a 417-foot-long station cavern when they designed and built that new station directly in front of the apartment towers in the 13^th District.

The Parisian transit agency expects the new Maison Blanche stop will be used by at least 65,000 riders daily. That’s more than the MTA expects at any East Harlem station.

Upsizing the French design to fit the Q’s 600-foot trains would increase the cost to approximately $280 million, The Post’s analysis showed.

Ditto London, where the transit agency fit a 400-foot platform into a 470-feet long station cavern at the new Nine Elms station, which was built to fuel the redevelopment of a once-industrial part of the British capital.

A version of the British design sized to fit the Q would cost approximately $350 million, the analysis showed.

The MTA refuses to say how much of the $7.7 billion budget for the East Harlem extension will go to new stations, but agency officials and experts agree they will account for the bulk of the cost.  

The Post’s investigation builds on work Goldwyn’s team at NYU, which detailed how excessive designs compound construction cost disadvantages the MTA already faces from union work rules and local limits on blasting and hauling.

Their 424-page report also revealed that the MTA is far more dependent on consultants than its global peers to develop projects, a setup that puts outside firms with little incentive to minimize costs and designs in the driver’s seat.

MTA officials attacked the findings and argued the new third track on the Long Island Rail Road’s Main Line in Nassau shows the MTA is delivering projects on time and on budget.

“You have to be careful with that subculture,” Lieber told The Post editorial board in February, derisively referring to the researchers. “Those people get a lot of their cost information from the Internet.”

A presentation by MTA construction czar Jamie Torres-Springer in December repeatedly referenced London and Paris as appropriate points of cost comparison for the MTA.

But that didn’t stop the agency from dismissing The Post’s investigation, which focused on the agency’s own benchmarks.

“The goal of the procurement process is to get the best value from qualified bidders and we encourage contractors on the Post’s list of preferred builders to bid at the same rates they offered elsewhere,” said Torres-Springer in a statement.