Since the 1960's, the Chevy TH400 transmission (Turbo Hydramatic) has been bolted to small and big block horsepower monsters and handled it well. A 3 speed transmission, the TH400 is the stronger cousin of the TH350. Few can complain with the performance of the TH400 and the available upgrades to let it perform reliably behind big horsepower engines are plenty. By the 1980's, fuel mileage concerns were driving the change to 4 speed overdrive transmissions. Many muscle cars, trucks and drag cars use the TH400.
There are some good reasons the TH400 can be abused to a degree. The TH400 is one tough customer because of the Simpson gear set and some structural design choices that make it strong. While the outside case of the TH400 is aluminum, a cast iron center support added superior strength. Couple that structural strength with a roller clutch that distributes the reactive force of the engine torque throughout the aluminum case. This means the whole unit is better able to handle added torque and repeated launches, exactly what you need for a tough everyday transmission and a performance trans.