LeBron James has the most games with 10+ rebounds, 20+ points and 5+ assists, with 250 games.

most games with 20 pts 10 rebs 5 asts
Interpreted as:
most regular-season games by a player with 20 or more pts 10 or more rebs 5 or more asts
JamesGarnettMaloneBarkleyWestbrookBirdWebberAntetokounmpoDuncanOlajuwonJokicO'NealDurantDrexlerJordanHardenRobinsonGriffinJohnsonHillCousinsWalkerPippenGasolNowitzki25024321621620119115913811811511111097959489898886827977767464
NAMEGPPTSREBASTMPGPPGRPGAPGSPGBPGTPGFGMFGAFG%3PM3PA3P%FTMFTAFT%MINSTLBLKTOVPF+/-
LeBron JamesLeBron James2507,5272,9162,15940.130.111.78.61.60.93.811.021.551.01.75.034.26.59.071.910,033394224949465+1562
Kevin GarnettKevin Garnett2436,0913,5091,58140.525.114.46.51.41.62.79.818.752.20.20.730.75.36.679.89,848336400651628+1674
Karl MaloneKarl Malone2166,2102,7651,29840.228.812.86.01.40.93.110.820.153.90.10.229.47.19.673.98,681300189674663+613
Charles BarkleyCharles Barkley2165,9033,1251,43841.527.314.56.71.91.13.69.717.057.20.62.427.17.39.774.58,972415228780655+168
Russell WestbrookRussell Westbrook2016,0632,5122,17937.730.212.510.81.60.45.010.723.345.81.85.433.17.09.078.37,570326711,004552+793
Larry BirdLarry Bird1915,5622,4301,45640.929.112.77.611.422.151.31.02.540.25.46.090.17,819443
Chris WebberChris Webber1594,2271,9921,07941.726.612.56.81.71.83.011.121.651.20.31.032.94.16.068.66,634268292482527+884
Giannis AntetokounmpoGiannis Antetokounmpo1384,1561,8881,00335.430.113.77.31.51.43.510.919.257.10.93.228.97.310.371.04,888202198480410+1287
Tim DuncanTim Duncan1183,1191,68869639.826.414.35.90.82.63.010.118.754.00.00.215.46.28.672.24,69396308350339+945
Hakeem OlajuwonHakeem Olajuwon1153,3371,65168941.229.014.46.02.04.03.411.621.254.70.00.125.05.77.775.04,735235465393407+90
Nikola JokicNikola Jokic1113,0101,44391235.327.113.08.21.40.83.310.318.057.31.53.840.55.05.885.83,91515593366314+871
Shaquille O'NealShaquille O'Neal1103,1721,55065140.328.814.15.90.73.13.011.619.958.20.00.020.05.611.150.54,43281340326333+714
Kevin DurantKevin Durant972,9911,12466039.230.811.66.81.11.43.710.420.251.42.45.742.07.68.788.13,805106139361207+810
Clyde DrexlerClyde Drexler952,6191,07370140.127.611.37.42.40.83.210.521.149.90.72.427.75.87.676.43,814227723052870
Michael JordanMichael Jordan943,1601,10376540.933.611.78.12.60.93.012.524.650.80.82.038.87.89.185.93,84224389280279+26
James HardenJames Harden893,0371,00991938.634.111.310.31.80.85.210.121.846.24.010.537.610.011.586.43,44016372462249+764
David RobinsonDavid Robinson892,5611,23055141.628.813.86.21.83.73.210.119.552.10.10.237.58.411.076.53,698163327284254+6
Blake GriffinBlake Griffin882,3511,08056837.426.712.36.50.80.52.710.019.052.40.82.334.26.08.670.33,2887448235282+730
Magic JohnsonMagic Johnson862,2669761,07940.026.311.312.59.217.352.90.61.929.87.48.587.33,438199
Grant HillGrant Hill822,10299262941.125.612.17.71.50.63.69.217.951.60.10.621.77.09.276.13,36812753297226+334
DeMarcus CousinsDeMarcus Cousins792,1461,12051536.627.214.26.51.71.54.79.419.248.81.23.634.57.29.377.12,893132117370309+351
Antoine WalkerAntoine Walker772,01794753743.326.212.37.01.60.83.610.122.644.62.26.236.13.85.470.73,33612359275223+261
Scottie PippenScottie Pippen761,90889953740.925.111.87.12.41.13.49.719.350.21.13.036.64.66.472.83,10918582257232+111
Pau GasolPau Gasol741,76593447139.223.912.66.40.72.22.99.016.654.10.20.537.15.87.280.12,90255165211167+377
Dirk NowitzkiDirk Nowitzki641,81277138040.828.312.05.91.11.52.09.719.948.61.43.540.47.68.589.12,6137296130148+636
StatMuse has game-level data for assists and rebounds going back to the 1982-83 season.