Banks are handing out mortgages of as much as $10 million to the wealthy in record numbers while first-time homebuyers struggle to get loans.

Erin Gorman, managing director at Bank of New York Mellon Corp., said she’s fielding more requests for home loans of at least $2 million than ever before. She recently provided a mortgage of more than $6 million for a client’s purchase of a second property in Colorado.