Four and three engined planes are only required to be able to continue a takeoff if one engine is shut down during flight. It's the same requirement as for twin engined aircraft. That's why twin engined planes have more power available during normal flight and can climb to cruising altitude faster. Boeing built the 707 to be about the maximum size possible using four engines available in the mid 1950's. In fact it used the same engines as the B-52. Douglas designed their DC-8's to be stretched in the future when better engines became available. Due to the shorter landing gear on the 707's, it would have been much more difficult for Boeing to stretch the 707.
I meant to say
Four and three engined planes are only required to be able to continue a takeoff if one engine is shut down during takeoff.