AN ACR PILOT SUGGESTS ALL PILOT'S ATTENTION BE ON TAXI TASKS WHILE IN THE RWY ENVIRONMENT AFTER AN OVERLOADED FO COULD NOT ASSIST HIM AVOID A NEAR RWY INCURSION.

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LANDED IN ZZZ. TWR INSTRUCTED TO TAXI TO A HOLD SHORT OF XXL. HELD SHORT OF RWY XXL. XY TWR INSTRUCTED US TO SWITCH TO RWY XXL TWR. XXL TWR INSTRUCTED US TO CROSS RWY XXL AND HOLD SHORT OF RWY XXR. AFTER XING RWY XXL; WE STOPPED SHORT ON THE RWY SIDE OF THE HOLD SHORT LINE. AFTER A VERY SHORT TIME; I RECOGNIZED THE ERROR AND CONTINUED. AS THE ACFT BEGAN TO MOVE; TWR ALSO CAUGHT THE ERROR AND ISSUED INSTRUCTIONS TO MOVE IMMEDIATELY. WE MOVED AND WERE WELL CLR OF THE RWY BEFORE LNDG TFC TOUCHED DOWN. IF I REMEMBER CORRECTLY; WHEN TWR CALLED; THE LNDG TFC WAS 3 MI OUT. AFTERWARD; WE CONTINUED UNEVENTFULLY TO THE GATE. I RECOGNIZED MY ERROR ON MY OWN; ALTHOUGH NO MORE THAN 15 SECONDS BEFORE ATC ALSO RECOGNIZED THE ERROR. I APPLIED MAX TAXI PWR AND MOVED. I WAS ALREADY MOVING WHEN ATC CALLED. HAD WE BEEN OPERATING WITH BOTH ENGS; I BELIEVE THAT WE COULD HAVE MOVED EVEN PRIOR TO ATC NOTICING THE SIT; HOWEVER IT TOOK A FEW MORE SECONDS TO GET THE ACFT IN MOTION WITH ONLY 1 ENG. THIS HAPPENED BECAUSE I BECAME DISTR AFTER ISSUING REPEATED INSTRUCTIONS TO THE FO WHO WAS ATTEMPTING TO WORK BOTH TWR AND OPS FREQS. I HAD TOLD HIM THAT I WAS COVERING ATC; YET HE CONTINUED TO TRY AND WORK BOTH RADIOS. I HAD ASKED HIM TO INFORM TWR -- GND THAT OUR GATE MIGHT NOT BE AVAILABLE IN ORDER TO ALLOW ATC TO TAXI US TO A CONVENIENT LOCATION WHILE WE AWAITED A GATE. I DIDN'T WANT TO ARRIVE AT THE RAMP AND THEN CREATE A TFC JAM DUE TO AN UNAVAILABLE GATE; AND WAS ATTEMPTING TO AVOID THAT SIT. PAST EXPERIENCE TOLD ME THAT ZZZ ATC WOULD SOMETIMES TAKE SUCH A DELAYED ACFT AND TAXI THEM ALL THE WAY W ON THE TXWY BTWN RWYS XXL AND XXR; SO I WAS TRYING TO MONITOR THE FO'S ATTEMPTS TO REACH OPS AND GET A WORD IN EDGEWISE WITH ATC AND ENDED UP STOPPING SHORT OF THE RWY BOUNDARY LINE. THE SOP MANUAL AND THE GND'S OPERATING MANUAL NEED TO BE MORE SPECIFIC REGARDING THE PM'S ROLE REGARDING COMPANY COM DURING HIGH INTENSITY TAXI OPS. MY ATTN BECAME DISTR BY AN FO WHO WAS TRYING TO DO TOO MUCH. MAYBE THE SOP SHOULD BE THAT WE DON'T DIVIDE OUR ATTN WITH COMPANY; RAMP CONCERNS UNTIL AFTER CLRING ALL RWYS ON TAXI IN.