In this study we consider the stabilization of n th-order linear time-invariant (LTI) dynamical systems using Multiplicity-Induced-Dominancy (MID)-based controller design in the presence of delays in the input/output channels. A sufficient condition is given for the dominancy of a real root with multiplicity n + 1 using an integral representation of the corresponding characteristic function. Furthermore, this sufficient condition is analyzed in the case when the characteristic function of the open-loop system is real-rooted, and delay intervals are derived for the set of parameters satisfying stabilizability and dominancy conditions. The efficiency of the proposed controller design is shown in the case of a multi-link inverted pendulum.