A PIPER PLT IS CLRED ONTO RWY WITH A CESSNA ON FINAL. THE CESSNA IS TOLD TO GO AROUND.

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IN PIPER ARROW ON MORRISTOWN GND FREQ 121.7; MY PAX; ANOTHER PLT; AND I REQUESTED PROGRESSIVE TAXI TO THE ACTIVE RWY. ENRTE TO RWY 31; WE WERE INSTRUCTED 'PROCEED ON TXWY B AND HOLD SHORT OFF OF RWY 5;' WHICH WE FOLLOWED. WE WERE INSTRUCTED TO 'CROSS RWY 5;' WHICH WE FOLLOWED. AFTERWARDS; WE WERE INSTRUCTED BY MORRISTOWN GND TO REMAIN WITH THEM. WHILE STATIC A FEW YARDS AWAY FROM THE HOLD SHORT LINES OFF OF RWY 31; WE RECEIVED OUR IFR RELEASE CLRNC FROM MORRISTOWN GND CTL AND HEARD MORRISTOWN GND CTL INSTRUCT US TO 'POS AND HOLD ON RWY 31 AND SWITCH TO TWR FREQ 118.1.' AFTER A CESSNA HAD JUST LANDED ON RWY 31; MY PAX; ANOTHER PLT; RESPONDED TO GND BY SAYING POS AND HOLD ON RWY 31. AS WE TAXIED ONTO RWY 31 AS INSTRUCTED AND CHKED IN WITH MORRISTOWN TWR; WE WERE THEN INSTRUCTED BY THE TWR TO TAXI OFF OF RWY 31; TO THE NEXT L TXWY. AS WE TAXIED OFF OF RWY 31; A FEW MOMENTS LATER; A CESSNA WAS INSTRUCTED TO 'GO AROUND.' AFTER WE TAXIED BACK ONTO TXWY B; WE WERE AGAIN CLRED AND INSTRUCTED TO TAKE OFF OF RWY 31. WE THEN DEPARTED MMU AND RETURNED TO BLM WITHOUT ANY DIFFICULTY.