<p>This article proposes a flexible semiparametric framework for a simple step-stress accelerated life-testing experiment in the presence of competing risks data. The stress is assumed to change from an initial level to a higher level at a pre-specified time. Instead of assuming a single parametric form for the hazard function at each stress level, it is assumed that the underlying lifetime distribution has a piecewise monotone hazard function. Within each sub-interval, the cause-specific hazard rates are assumed to follow a piecewise monotone hazard function. This framework provides a good approximation to a broad class of hazard functions and allows the failure rate to exhibit increasing, decreasing, constant, unimodal, bathtub shape etc. over time, depending on the underlying failure mechanism. It is a natural generalization of the piecewise constant hazard function. The piecewise constant hazard function can be obtained as a special case. We develop both classical and Bayesian inference procedures for the proposed framework. In the classical framework, maximum likelihood estimation is used to estimate model parameters, and their asymptotic confidence intervals are constructed. Bayesian inference is carried out by assuming a flexible prior distribution. We obtained the Bayes estimates and the associated credible intervals for the model parameters under the squared-error loss function. The performance of the proposed estimators has been examined through an extensive simulation study. In practice, the locations of the cut points are often unknown and play a crucial role in model performance. So, we address this issue by determining optimal cut points using a non-homogeneous Poisson process. Two real-life dataset is analyzed to illustrate the practical applicability and effectiveness of the proposed methodology. The results are quite satisfactory.</p>