  In this work, we explore the prospect of generalizing the constant-roll
condition in canonical inflationary model to non-canonical models. To find a
natural generalization, we focus on three manifestations of this condition and
construct constant-roll models corresponding to each manifestation. These
models are not equivalent but reduce to the familiar constant-roll model in
canonical limit. To showcase the applicability of our generalized mechanism, we
examine a specific class of non-canonical models, which can be viewed as
extensions of k/G inflation. In these models sound speed is constant. We
conduct a comparative study, and with an analytical examination of the model,
specify instances when our constant-roll conditions yield dissimilar outcomes
and when they exhibit analogies. We also apply our findings to scrutinize
another kinetically driven inflationary model with varying sound speed. We
demonstrate that each of our constant-roll conditions leads to a unique set of
solutions. Afterward, we construct a four-stage constant-roll kinetically
driven inflation that complies with CMB constraints, it sustains for a
sufficiently long period of time, and finally gracefully exits. In this model
the spectrum of curvature perturbations is enhanced in a brief phase of
non-slow-roll inflationary evolution. Employing numerical methods, we analyse
this scenario to elucidate how altering the constant-roll condition impacts the
power spectrum and the model's dynamics.
