Michael Vick rushed for the most yards by a quarterback when playing 2+ seasons, with 6,109 yards.

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which qb has the most rushing yards in two seasons
Interpreted as:
Which qb has the most rushing yards in two or more seasons?
VickNewtonCunninghamWilsonYoungTarkentonJacksonMcNairMcNabbElwayRodgersRoteHarbaughLandryDouglassCulpepperFitzpatrickStewartSmithLayneGannonBrunellKaepernick6.1k5.5k4.9k4.6k4.2k3.7k3.6k3.6k3.5k3.4k3.3k3.1k2.8k2.7k2.7k2.7k2.6k2.6k2.6k2.5k2.4k2.4k2.3k
NAMEGPRUSH YDSSEASATTYPCRUSH YDS/GRUSH TDREC YDSRECTRGAVGREC YDS/GREC TD
Michael VickMichael Vick1436,109138737.042.7361220.50.00
Cam NewtonCam Newton1435,463111,0875.038.273683322.70.51
Randall CunninghamRandall Cunningham1614,928167756.430.635-620-3.00.00
Russell WilsonRussell Wilson1524,624108295.630.42220445.00.11
Steve YoungSteve Young1694,239157225.925.1432201.00.00
Fran TarkentonFran Tarkenton2463,674186755.414.932-1200.00
Lamar JacksonLamar Jackson563,61346056.064.5210020.00
Steve McNairSteve McNair1613,590136695.422.3374114.00.00
Donovan McNabbDonovan McNabb1673,459136165.620.729-758-1.40.00
John ElwayJohn Elway2343,407167744.414.63361320.30.31
Aaron RodgersAaron Rodgers2083,347176765.016.134-1133-3.7-0.10
Tobin RoteTobin Rote1493,128136354.921.03728214.00.21
Jim HarbaughJim Harbaugh1772,787145615.015.718-820-4.00.00
Greg LandryGreg Landry1462,655154306.218.221000.00
Bobby DouglassBobby Douglass912,654104106.529.222-21-2.00.00
Daunte CulpepperDaunte Culpepper1052,652115145.225.3340110.00.00
Ryan FitzpatrickRyan Fitzpatrick1662,625175744.615.821-333-1.00.00
Kordell StewartKordell Stewart992,61795065.226.432130101813.01.31
Alex SmithAlex Smith1742,604145804.515.015-733-2.30.00
Bobby LayneBobby Layne1752,451156114.014.025000.00
Rich GannonRich Gannon1572,449165214.715.621-321-1.50.00
Mark BrunellMark Brunell1932,421175134.712.5150000.00
Colin KaepernickColin Kaepernick692,30063756.133.3130000.00
Roger StaubachRoger Staubach1312,264114105.517.320-131-13.0-0.10
Terry BradshawTerry Bradshaw1682,257144445.113.432100.00
StatMuse has season-level data for rushing yards going back to the 1932 season.