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In this work, we explore the prospect of generalizing the constant-rollcondition in canonical inflationary model to non-canonical models. To find anatural generalization, we focus on three manifestations of this condition andconstruct constant-roll models corresponding to each manifestation. Thesemodels are not equivalent but reduce to the familiar constant-roll model incanonical limit. To showcase the applicability of our generalized mechanism, weexamine a specific class of non-canonical models, which can be viewed asextensions of k/G inflation. In these models sound speed is constant. Weconduct a comparative study, and with an analytical examination of the model,specify instances when our constant-roll conditions yield dissimilar outcomesand when they exhibit analogies. We also apply our findings to scrutinizeanother kinetically driven inflationary model with varying sound speed. Wedemonstrate that each of our constant-roll conditions leads to a unique set ofsolutions. Afterward, we construct a four-stage constant-roll kineticallydriven inflation that complies with CMB constraints, it sustains for asufficiently long period of time, and finally gracefully exits. In this modelthe spectrum of curvature perturbations is enhanced in a brief phase ofnon-slow-roll inflationary evolution. Employing numerical methods, we analysethis scenario to elucidate how altering the constant-roll condition impacts thepower spectrum and the model's dynamics.

Analytical Insights into Constant-Roll Condition: Extending the Paradigm to Non-Canonical Models