TXWY EXCURSION IN A NIGHT OP BY ACR MLG DURING A TIGHT TURN. ARPT PROB TXWY RAMP.

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FLT DEPARTED MSP AT PM59Z AND LANDED IN RST AT AM28Z. THE FLT WAS NORMAL. WE TAXIED BACK ON TXWY A. THE CAPT DECIDED TO ENTER THE RAMP VIA TXWY E. THIS ALLOWED FOR A STRAIGHT-IN APCH TO THE JETWAY RATHER THAN MAKING A HARD R TURN TO GET TO THE JETWAY. THERE WAS ALSO ANOTHER COMPANY ACFT PARKED ON THE RAMP THAT WOULD HAVE ALSO HAMPERED A HARD R TURN TO THE JETWAY. THE TURN FROM TXWY A ONTO TXWY E IS APPROX 135 DEGS. BOTH TXWYS ARE RATHER NARROW. WHEN THE CAPT TURNED THE AIRPLANE AND WENT THROUGH APPROX 45 DEGS OF TURN I SAID TO STRAIGHTEN IT OUT THAT I DIDN'T THINK WE WOULD MAKE IT. I TOLD HIM TO STRAIGHTEN IT OUT AGAIN WHICH HE DID. HE DECIDED TO STOP THE AIRPLANE AND DID STRAIGHTEN THE NOSEWHEEL OUT. THE AIRPLANE WAS NOW AT ABOUT 90 DEGS THROUGH THE TURN. JUST AS THE AIRPLANE WAS ALMOST STOPPED THE R MAIN ROLLED OFF THE HARD TAXI SURFACE ONTO THE SOFTER DIRT. WE DID NOT ATTEMPT TO PROCEED ANY FURTHER. THE AIRPLANE WAS SHUT DOWN AT THIS POINT. APU WAS STARTED AND PAX WERE DEPLANED IN A NORMAL FASHION THROUGH THE FORWARD AIRSTAIRS AND TAKEN TO THE TERMINAL ON AN ARPT BUS. THE ACFT WAS TURNED OVER TO MAINT AT THIS TIME. THE ARPT DRIVER THAT TOOK US INTO THE TERMINAL DID SAY THIS WAS NOT THE FIRST TIME THIS HAD HAPPENED AT THIS INTXN.