Studies on the self-leveling behavior of debris bed are crucial in the assessment of core-disruptive accident (CDA) that could occur in sodium-cooled fast reactors (SFR). In our previous publications, a simple empirical model, with its wide applicability confirmed over various experimental conditions, has been successfully proposed to predict the transient leveling behavior. However, up until now this model is restricted to beds of spherical particles. Focusing on this aspect, based on the existing experimental knowledge obtained, in this study a methodological framework is proposed with the purpose of extending its predicative capability to cover non-spherical particles. The proposed framework principally consists of two empirical terms - with one for correcting the terminal velocity of a single non-spherical particle, which is the key parameter in our modeling, and the other for representing the additional particle-particle interactions caused by the shape-related parameters. Through the preliminary analyses, it was found that by linking the Geldart's method with our recently developed pressure-drop measurement facility, the terminal velocity of irregularly-shaped particles can be readily achieved, while for modeling the additional particle-particle interactions, based on the latest data available a parametric study is also conducted to identify the potential contributors. Although further investigations would be necessary, the current study confirms the possibility and provides a guideline for our future studies regarding empirical model development for predictions of debris bed self-leveling behavior within more realistic conditions.