The subway’s signaling system is so old that, when parts fail — as they do with increasing frequency — it’s hard to find replacements because vendors don’t make them anymore. Subway cars are of a more recent vintage, but the oldest among them break down often. And then there are the decrepit stations, which are unpleasant at best; for people in wheelchairs or with baby strollers, they’re hostile terrains of leaky passageways and steep stairs, with few operational elevators to be found. In the rare instance when the M.T.A. has built new lines, like the one along Second Avenue that opened in 2017 after decades of delays, the agency managed to spend vastly more per mile of track than other transit systems around the world have spent.

Enter Andy Byford, a thoughtful and serious transportation specialist whom the M.T.A. hired from Toronto to oversee New York’s subway and bus system. Mr. Byford’s plan, called Fast Forward, outlines rapid-fire upgrades. Within five years, the M.T.A. would install a modern switching system on five high-traffic subway lines, upgrade 150 stations, make 50 stations wheelchair-accessible, buy 650 new subway cars and redesign bus routes in all five boroughs. Most of the rest of the system would be upgraded over the following half decade.

This is an impressive to-do list, but the most important part of Mr. Byford’s plan entails overhauling how the transit system buys equipment, hires contractors, negotiates with unions and manages big projects. The M.T.A. won’t accomplish a fraction of what’s in Fast Forward if it uses the same approach officials have applied in building the first phase of the Second Avenue line or East Side Access, the much delayed and over-budget project that will — some day — bring the Long Island Rail Road to Grand Central Terminal.

Mr. Byford and other M.T.A. officials are not saying how much this plan will cost, but experts say it could top $40 billion. While that is a lot of money, New York can afford it — the state budget for the 2019 fiscal year is $170 billion, and Mayor Bill de Blasio has proposed a $89 billion city budget. (The M.T.A. is funded by fares, tolls, taxes and grants from the state and local governments.) Besides, there is little choice but to invest in the transit system, without which the region would grind to a halt.

A few ideas for how elected officials can come up with the money: The Legislature could pass the comprehensive congestion pricing plan proposed by Mr. Cuomo’s Fix NYC panel of experts earlier this year — doing so would raise $1.5 billion a year, according to Charles Komanoff, a transportation analyst and advocate. Where new or much improved subway lines would increase property values and taxes significantly, a portion of the additional revenue could be used to help pay off bonds that financed the project. Former Mayor Michael Bloomberg worked with the M.T.A. in utilizing that approach to help pay for the extension of the 7 line to the Far West Side of Manhattan, completed in 2015. Cities, including New York, also have used sales and payroll taxes, taxi surcharges and car registration fees to pay for transit investments. In 2016, for example, voters in Los Angeles and Seattle approved ballot proposals to raise sales and other taxes to pump $120 billion and $54 billion, respectively, into their transit systems.