Prof. O’Hara said the gusher of public and available data opens new avenues to a far more accurate census, but only if the numbers can be proven accurate and the Census Bureau can navigate the tricky boundary between tapping private research and issuing public statistics.

“There is no significant buy-in yet” to major changes in the census, Terri Ann Lowenthal, a longtime census expert and consultant to governments, businesses and other census “customers,” said in an email. “Too early without research, testing and transparency on those sorts of questions. And there probably will be even greater caution about using third-party commercial data.”

That said, she added, many users of census data agree that better use of outside records, conducted in a way that preserves privacy and credibility, could increase the accuracy of the head count and reduce its staggering cost — $14.2 billion, or about $117 per household counted in the 2020 census.

What seems clear is that the existing way of tallying the nation’s population is pressing its limits. The first census by mail was conducted in 1960. Ever since, the nation has counted itself by tallying census forms filled out on millions of kitchen tables, then dispatching an army of census takers to collect data from the millions of others who didn’t fill them out.

The 2020 census streamlined that process by moving most of the form-filling from cumbersome paper surveys to the internet, and equipping census workers with iPhones and census-taking apps instead of clipboards and paper forms. Online census forms proved a resounding success, census officials say, because they were easier, cheaper and quicker to process, and because the Census Bureau’s computer operations handled them virtually without problems.

Yet despite those improvements, the share of residents who opted to complete census forms remained stuck at two-thirds of all households, where it has sat stubbornly for four decades. The so-called nonresponse follow-up, known as NRFU, of the remaining third, conducted by census workers, was hamstrung by hurricanes, forest fires, political interference and rising suspicion of the government among partisans on the political right and among racial and ethnic groups.

Steve Jost, a former senior census official who is a consultant to the Census Project, a group advocating a more accurate count, lamented that. Tracking down nonresponders eats up roughly half the cost of each census, he said, yet the census still fails to reach 2 to 3 percent of households.