By Chad Terhune and Julie Appleby Kaiser Health News

NEW YORK (CNNMoney) -- Health savings accounts are poised for a major expansion by Republicans in Washington, D.C., and that could mean millions more customers — and fees — flowing to a handful of companies.

Investors are betting on it, bidding up shares of HSA provider HealthEquity by about 35% since the November election. It's one of the best performing stocks on Wall Street since Donald Trump won the White House.

Another big beneficiary might be Optum Bank, the industry leader, with more than 3 million of these accounts and about $7 billion in assets it manages for consumers. It's owned by the nation's largest health insurer, UnitedHealth Group.

For years, these companies and others have been lobbying lawmakers for changes that could become reality with a Republican-controlled Congress and Trump administration.

The GOP health law replacement plan introduced Monday in the House reflects the party's broad consensus for giving more Americans access to HSAs, which allow people to put aside money tax-free for medical expenses.

"There is an excitement in the business now," Dr. Steve Neeleman, founder of Utah-based HealthEquity and a former trauma surgeon. "There are definitely things Washington can do to make HSAs more enticing to a broader market."

Health saving accounts were introduced in 2003 in legislation championed by President George W. Bush. Enrollment has grown steadily to nearly 21 million accounts with $41 billion in assets, according to the Devenir Group, a research and consulting firm that tracks the industry.

Still, that number is a small fraction of the 178 million people who have health insurance through their jobs or purchase it on their own.

Industry officials are eager to reach new markets, including baby boomers in Medicare and enrollees in the military's Tricare system, for whom — under current law — HSAs are off-limits. They also want to manage larger accounts that generate more revenue. Republican proposals in Congress could help accomplish both.

Proponents say consumers with HSAs may be more judicious in using services and seeking lower prices because their own money is at stake. Backers also like the tax breaks: There's no tax on the funds' investment gains or on withdrawals if spent on medical care. But critics note this treatment favors the wealthy as those with lower incomes often struggle to afford health care and have little to set aside in savings accounts.

A 2015 study found that high-income households were considerably more likely than low-income to contribute to HSAs. The highest-income tax filers were also substantially more likely to fund their accounts fully.

Under current law, HSA accounts must be paired with a high-deductible health plan. Individuals can contribute as much as $3,400 annually, or $6,750 for families. Unused balances roll over to the following year, and consumers can take the account with them when they leave an employer, much like a 401(k) retirement account. Some employers contribute to HSAs on behalf of their employees.

The House Republican plan proposes to nearly double the HSA contribution limits to at least $6,550 for individuals and $13,100 for families beginning in 2018. Meanwhile, in the Senate, other proposals — including one by Sen. Rand Paul (R-Ky.) and another advanced by Sens. Bill Cassidy (R-La.) and Susan Collins (R-Maine) — lay out slightly different yet favorable treatment of HSAs.

The over-65 market in Medicare is a prime target for expansion.

"That is a great population that has the potential to save and really take more control over their health care," said Eric Remjeske, president of the Devenir Group, the research and consulting firm.

Neeleman agreed and said it's wrong to shut out thousands of Baby Boomers who are retiring every day. "It's just not fair," he said. Backers note that, even though Medicare is not a high-deductible health plan, there is cost sharing in Medicare, which leads many in Congress to think the prohibition should be abandoned.

It's already a lucrative business. In a February investor presentation, HealthEquity touted a gross profit margin of 57% on its 2.7 million health savings accounts. And the company said the accounts become more profitable over time, reaching a 72% profit margin six years in as costs decrease and balances grow.

The companies overseeing these accounts rake in money from a variety of fees, much like banks do.

Often consumers pay service fees that range from $2 to $5 per month for each account. The companies also earn interest on the customers' money they manage in what's known as "custodial" revenue. And HSA administrators collect fees from merchants when consumers use company-issued debit cards to pay for medical expenses out of their accounts.

At HealthEquity, the second-largest HSA provider, about half of its revenue comes from service fees and the rest is derived from custodial revenue or debit fees, according to its annual report.

Companies can also earn fees from mutual funds offered to customers as investment options. In the workplace, some employers cover some or all of the fees for workers.

Neeleman said that HealthEquity and other firms provide an important service and that they're upfront about the fees they collect. Optum declined to comment for this story.

In addition to well-heeled retirees on Medicare, companies running these accounts also see opportunity among lower-income households.

Several states have experimented with adding savings accounts in Medicaid, the state-federal insurance program for the poor. Vice President Mike Pence embraced this idea while he was governor of Indiana. Medicaid members in Indiana can get additional benefits such as vision and dental coverage if they make small monthly contributions to accounts similar to HSAs. However, debate continues as to how effective the approach will be for this population.

Industry officials doubt they will get everything on their wish list from Congress. For instance, unlimited contributions to tax-free accounts could cost the federal government too much in revenue and invite more criticism that HSAs are a tax shelter for the rich.

Kevin Robertson, a senior vice president and director of sales for HSA Bank, the industry's third-largest company, said some proposals are "more likely wishful thinking" but the overall direction is unmistakable as the GOP pushes a market-driven approach to health care.

"The political and economic winds are favorable and most definitely pushing HSAs," he said.

Kaiser Health News is national health policy news service that is part of the nonpartisan Henry J. Kaiser Family Foundation.

TM & © 2017 Cable News Network, Inc., a Time Warner Company. All rights reserved.