One think to remember is that performance calculations take into account the loss of power on one engine at decision speed (V1). In a twin, you loose half the power whereas in a four jet, you only lose a quarter. For this reason, four jets can be less powerful and will consequently have flatter initial climbs on all engines. A good example of this is the A330/340-300. Essentially the same airframe except that the the 330 has 2 x 70,000lbs of thrust whereas the 340 has 4 x 30,000lbs of thrust. Despite having 20,000lbs less thrust, the 340 can lift about 35 tonnes more than the 330. Also, the point at which VR (rotate speed) will be reached is further down the runway.
However, it doesn't explain the OPs concern. Here's a link to a performance related incident.
Incident: Jet Airways B773 at London on Aug 30th 2016, unsafe departure