Semi-compensatory models show promise in representing two-stage choice processes by integrating choice set formation within discrete choice models. However, they are subject to simplifying assumptions that limit their application. The current study proposes a novel semi- compensatory model that alleviates these simplifying assumptions concerning (i) the number of alternatives, (ii) the representation of choice set formation, and (iii) the error structure. The proposed model represents a sequence of choice set formation based on the conjunctive heuristic with correlated thresholds, and utility-based choice accommodating alternatively nested substitution patterns across the alternatives and random taste variation across the population. The model is accompanied by an innovative two-stage procedure to collect data about semi-compensatory choice processes in a digital economy environment. The proposed model is applied to off-campus rental apartment choice of students in a university city in the core of medium-size metropolitan area.