The firms are pushing aggressively into “asset-based finance,” a kitchen sink of debt including auto loans, credit cards, real-estate mortgages and loans backed by equipment such as fiber-optic networks. Such financings touch almost every piece of the U.S. economy, and tapping into the market could mean riches for the fund’s executives and their shareholders.

If asset-based finance by private funds grows as quickly as corporate lending did, consumer, equipment and specialty lending by private funds could rise to $900 billion in the next few years from $350 billion currently, according to research by Atalaya Capital Management. The estimate doesn’t include residential and commercial mortgages, which many of the funds also buy.

Apollo Global Management Chief Executive Marc Rowan has led the charge—acquiring last year a division of Credit Suisse that was the biggest Wall Street producer of asset-based finance. Apollo’s stock price has since grown 60% and he has made personal paper gains of about $1.2 billion.

“Everywhere in the world, people are choosing more from the investment marketplace, less from the banking system,” Rowan said at an event hosted last month by the Economic Club of Washington, D.C.

Private-equity firms began replacing banks as the go-to providers of corporate loans after the 2008 financial crisis and began edging into asset-based finance in recent years. Banks still provide the lion’s share of the debt, but they have been scaling back.

Rising interest rates hit banks with heavy losses starting in 2022, triggering failures last year at institutions such as Silicon Valley Bank and a subsequent regulatory crackdown. Fintech companies such as Upstart that make consumer and mortgage loans also took a hit because they borrow money from banks and credit unions.

That gave private fund managers an opening at a critical time. The firms had raised $1.5 trillion from their clients to invest in private debt by the end of 2022, but $434 billion of the money was sitting idle, according to financial data company PitchBook. To charge fees on the capital, the fund managers needed to put it to work.

Asset managers have been hiring teams that can churn out asset-based finance and distribute it to their investment clients.

KKR nabbed Deutsche Bank’s structured-finance chief Dan Pietrzak in 2016 and now manages about $48 billion of asset-based investments. Sixth Street Partners recruited Credit Suisse’s structured-finance head Michael Dryden in 2022 and has built a 30-person asset-based finance team.

“Banks are less willing to hold these assets, and a handful of funds will become big scale players to fill those gaps,” said Sixth Street co-founder Michael Muscolino.

Asset-based finance also gives private funds a way to grow because they can sell it to large institutional investors who don’t buy junk-rated corporate debt—which the firms typically traffic in. Consumer and mortgage loans can be repackaged into complex instruments with investment-grade credit ratings often required by insurers, pensions and endowments.

A flood of deals has followed:

KKR bought $7.2 billion of loans backed by recreational vehicles from BMO in December after agreeing in June to purchase from PayPal up to $44 billion of existing and future buy-now-pay-later loans.

Apollo has rebranded as Atlas the Credit Suisse business it purchased, and has provided dozens of “warehouse” credit lines to companies backed by assets such as freight ships and solar power projects. The companies use the money to make loans to their customers that are eventually bundled up and sold to private credit firms or buyers of asset-backed bonds.

Sixth Street, Pacific Investment Management and KKR bought Goldman Sachs’s consumer lending unit GreenSky in October and took over $8 billion of its loans. Last month, Blackstone purchased $1.1 billion of credit card debt from the U.S. unit of Barclays.

Ares Management bought a $3.5 billion package of specialty loans from PacWest last summer before the ailing bank got sold. In December, Blackstone and Canada Pension Plan Investment Board purchased $17 billion of mortgages from the liquidation of Signature Bank.

Estimates of the total asset-based finance in the economy range from $25 trillion to $40 trillion. Private-credit executives say they ultimately hope to capture about one-quarter of that.

The trend is in an early phase, and banks still provide much of the loans. Credit card lending by U.S. banks increased last year as consumers took longer to pay off balances.

“An ever larger proportion of lending will be concentrated among a small group of large, influential asset managers,” Moody’s Ratings said in a report this week. “This will only fuel their influence in the economy.”

Private funds have increasingly joined up with insurance companies to boost their buying power. They are also using complex instruments to buy risk from big banks such as JPMorgan Chase, while banks are lending money to the funds to help them boost returns.

Senate Banking Committee Chair Sherrod Brown (D., Ohio) asked the Federal Reserve and other regulators in November to assess risks that private credit poses to the U.S. financial system. Regulatory response has been mixed.

Regulation of banks fueled much of the increased private-fund activity. A proposal in July—partially in response to the regional-bank crisis—increased the capital banks must reserve against “risk-weighted assets,” hurting profitability. It also made holding asset-based loans far less attractive for banks. The Fed announced last week that it plans to revise the proposal, dubbed Basel Endgame.

T.J. Durkin, head of asset-based finance at Angelo Gordon, assigned several of his staff last year to regularly visit regional banks and credit unions to sniff out new deals.

“The coverage model has flipped, with banks becoming a source of interesting assets for us to invest in,” he said.

Write to Matt Wirz at matthieu.wirz@wsj.com