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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WestbrookDoncicKiddJohnsonAntetokounmpoJokicHardenRondoBird922211111
NAMEGPPTSASTREBMPGPPGRPGAPGSPGBPGTPGFGMFGAFG%3PM3PA3P%FTMFTAFT%MINSTLBLKTOVPF+/-
Russell WestbrookRussell Westbrook919714815439.321.917.116.42.10.34.48.121.338.01.65.428.64.16.662.73531934026+107
Luka DoncicLuka Doncic261323135.830.515.516.01.00.05.510.524.043.83.08.037.56.58.081.37220115+2
Jason KiddJason Kidd240333247.020.016.016.52.00.05.57.518.540.53.58.043.81.53.050.09440113+14
Magic JohnsonMagic Johnson244323442.522.017.016.02.50.56.56.015.538.72.06.033.38.09.088.98551136
Giannis AntetokounmpoGiannis Antetokounmpo124151935.824.019.015.03.01.05.09.027.033.31.07.014.35.010.050.0363152+5
Nikola JokicNikola Jokic130171533.830.015.017.01.02.08.011.014.078.63.03.0100.05.05.0100.0341285+11
James HardenJames Harden153171642.153.016.017.00.00.08.014.026.053.89.016.056.316.018.088.9420082+13
Rajon RondoRajon Rondo118201747.818.017.020.01.01.04.07.020.035.00.00.04.07.057.1481143+5
Larry BirdLarry Bird130151744.030.017.015.01.03.04.011.020.055.00.03.00.08.08.0100.0441341
StatMuse has game-level data for assists and rebounds going back to the 1982-83 season.