MLG Y TAXI SPD ALMOST HAD GND COLLISION WITH ACR X. EVASIVE ACTION TAKEN BY BOTH ACFT EXCESSIVE BRAKING.

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AFTER LNDG RWY 28L CLRED ON HIGH SPD EXIT 'CY' TAXI E ON 'C' TO 'VICTOR TAXIWAY' STILL WITH (TWR ATC). TOLD TO EXPEDITE ACROSS RWY 28C ON VICTOR. TFC ON LESS THAN 2 MI FINAL RWY 28C. CONTACT GND WHEN CLR ON RWY 28C. JUST AS WE WERE CLRING 28C TWR ASKED IF WE COULD STILL MAKE A R TURN EBOUND ON RWY 28C (IE; HEAD ON INTO LNDG TFC.). WE WERE PAST THE POINT AT WHICH THIS WAS POSSIBLE AND INFORMED TWR OF SAME. JUST AS WE APCHED POINT AT WHICH TAXIWAY VICTOR INTERSECTS TAXIWAY WHISKY I NOTICED COMPANY MLG APCHING US AT HIGH TAXI SPD OUT OF CORNER OF MY EYE HE WAS EBOUND ON WHISKY. WE WERE NEBOUND ON VICTOR. THUS HE WAS APCHING US FROM OUR (L) 8 O'CLOCK POS. BOTH CAPT AND I WERE LOOKING TO THE R SIDE OF OUR ACFT TO SEE IF WE COULD STILL MAKE THE QUICK R TURN ONTO RWY 28C. THE TWR NEVER (POINTED OUT) THE COMPANY MLG EBOUND ON WHISKY. I JUST SAW ACFT WITH MY PERIPHERAL VISION AND TOLD CAPT TO STOP IMMEDIATELY. THE OTHER ACFT STOPPED ABRUPTLY AT THE SAME MOMENT. I BELIEVE HE BEING N OF RWY 28L WAS COMMUNICATING WITH GND CTL. WE WERE STILL WITH TWR. I BELIEVE THIS NEAR COLLISION ON THE GND COULD HAVE BEEN EASILY AVOIDED IF THE TWR HAD JUST POINTED OUT THE OTHER JET AND TOLD US TO GIVE WAY OR VICE VERSA BUT OBVIOUSLY COORD BTWN THE TWR AND GND CTLRS WAS WEAK AND I FEEL RUSHED AND 2 ACFT OURS IN THE BLIND N TO THE OTHER WERE TOLD TO TAXI HURRIEDLY AT NIGHT. TO A NEAR COLLISION AND UNNERVING TO PAX. TO STOP AND AVOID POSSIBLE WING STRIKE OR WORSE. I AM VERY SURPRISED THE TWR DIDN'T JUST MENTION THE OTHER ACFT AND POTENTIAL CONFLICT TFC TO US INSTEAD OF ISSUING NUMEROUS CHANGING CLRNCS TO TRY AND AVOID IT! THIS WAS A VERY UNUSUAL EXPERIENCE AT PIT ARPT WHERE I HAVE MUCH EXPERIENCE. THE TWR/GND PERSONNEL GENERALLY ARE MORE INFORMATIVE TO US IN THESE SITUATIONS AND SUCH CLOSE CALLS ARE RARE OCCURRENCES. BUT STILL SERIOUS.