Russell Westbrook has the most games with 15+ assists, 15+ points and 15+ rebounds, with 9 games.

who has the most career games with 15 points, 15 assists and 15 rebounds
Interpreted as:
Who has the most career regular-season games with 15 or more points, 15 or more assists and 15 or more rebounds?
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Russell WestbrookRussell Westbrook919714815439.321.917.
Luka DoncicLuka Doncic261323135.830.515.516.
Jason KiddJason Kidd240333247.
Magic JohnsonMagic Johnson244323442.522.
Giannis AntetokounmpoGiannis Antetokounmpo124151935.824.
Nikola JokicNikola Jokic130171533.830.
James HardenJames Harden153171642.
Rajon RondoRajon Rondo118201747.818.
Larry BirdLarry Bird130151744.
StatMuse has game-level data for assists and rebounds going back to the 1982-83 season.