LeBron James has the most games in the NBA Finals with 10+ assists, 10+ points and 10+ rebounds, with 11 games.

most nba finals games with 10 point and 10 assist and 10 rebound or more
Interpreted as:
most NBA finals games by a player with 10 or more point and 10 or more assist and 10 rebound or more
JamesJohnsonGreenButlerBirdFrazierChamberlainRussellDurantCurryRondoDuncanKiddBarkleyPippenWorthyCowensUnseldBaylorWest118322222111111111111
NAMESERIESGPPTSASTREBMPGPPGRPGAPGSPGBPGTPGFGMFGAFG%3PM3PA3P%FTMFTAFT%MINSTLBLKTOVPF+/-
LeBron JamesLeBron JamesNBA Finals1132012313544.729.112.311.21.41.03.510.823.745.61.45.325.96.18.274.449115113926+29
Magic JohnsonMagic JohnsonNBA Finals81301189242.616.311.514.81.90.45.54.59.846.20.51.050.06.88.084.43411534428
Draymond GreenDraymond GreenNBA Finals337334042.012.313.311.02.31.05.74.310.740.61.03.727.32.74.066.7126731714+3
Jimmy ButlerJimmy ButlerNBA Finals275242346.037.511.512.03.51.54.012.519.564.10.51.533.312.013.092.3927382+25
Larry BirdLarry BirdNBA Finals254232645.527.013.011.53.50.02.59.021.541.91.03.033.38.08.594.1917058
Walt FrazierWalt FrazierNBA Finals225222441.512.512.011.05.511.547.81.53.542.9837
Wilt ChamberlainWilt ChamberlainNBA Finals226207148.513.035.510.05.09.055.63.013.023.1974
Bill RussellBill RussellNBA Finals242204948.021.024.510.08.011.072.75.08.062.5965
Kevin DurantKevin DurantNBA Finals120101237.620.012.010.01.03.02.07.017.041.20.03.00.06.06.0100.0381323+30
Stephen CurryStephen CurryNBA Finals132111036.332.010.011.01.00.08.07.017.041.24.011.036.414.014.0100.0361083+21
Rajon RondoRajon RondoNBA Finals119101242.019.012.010.02.01.03.08.018.044.41.01.0100.02.05.040.0422132+12
Tim DuncanTim DuncanNBA Finals121102046.021.020.010.00.08.04.09.019.047.40.01.00.03.05.060.0460842+11
Jason KiddJason KiddNBA Finals123101043.023.010.010.03.00.01.011.026.042.31.03.033.30.01.00.0433011+3
Charles BarkleyCharles BarkleyNBA Finals132101246.032.012.010.03.01.01.010.019.052.60.02.00.012.015.080.0463111
Scottie PippenScottie PippenNBA Finals115121242.015.012.012.02.02.07.05.012.041.70.00.05.07.071.4422274
James WorthyJames WorthyNBA Finals136101644.036.016.010.02.00.05.015.022.068.20.00.06.010.060.0442052
Dave CowensDave CowensNBA Finals125102148.025.021.010.01.00.011.020.055.03.04.075.048103
Wes UnseldWes UnseldNBA Finals111102339.011.023.010.03.012.025.05.08.062.5395
Elgin BaylorElgin BaylorNBA Finals113111245.013.012.011.04.013.030.85.06.083.3456
Jerry WestJerry WestNBA Finals142121348.042.013.012.014.029.048.314.018.077.8482
StatMuse has game-level data for assists going back to the 1960 Finals.