Even while struggling with its finances, the Metropolitan Museum of Art set a record for attendance, attracting 6.7 million visitors during the fiscal year that ended on June 30 — the highest number since the museum began tracking admissions more than 40 years ago, the Met announced on Thursday.

The total includes the museum’s three locations — the Met Fifth Avenue, the Met Cloisters and the new Met Breuer, which presents modern and contemporary programming and opened in March.

This year’s attendance — the fifth in a row exceeding six million — was 400,000 higher than that of the previous year. The Met attributed this to an increase of about 200,000 visitors at its Fifth Avenue flagship and the Met Cloisters combined and to 185,000 people taking in the Met Breuer during its first four months.

There are other factors in play: The increase took place in a year when a lawsuit forced the Met to more clearly explain its pay-what-you-like entrance policy, calling its $25 full-admission price “suggested” instead of “recommended.” (Signs now advise visitors that “The amount you pay is up to you.”)