Different rims are rated for different PSI levels. But, assuming a 140 PSI tire is the perfect width for a given rim, it probably is going to stay mounted without problems.
However, who NEEDS a PSI over 120 pounds? The best PSI level for a tire is the one that yields 15% deflection of the sidewalls under the rider's weight. With the 23mm tires popular with guys who pretend to race bikes, 15% deflection can be obtained at 70 PSI for light riders, and 90 PSI for average riders. A rider over 180 pounds might need to go as high as 120 PSI to get 15% deflection.