This study investigates the potential market demand of shared-ride taxi and shuttle services designed to serve members of organizations in dense urbanized areas. It develops and compares two different multivariate count data modeling approaches, the multinomial distribution and the full enumeration of count alternatives, under an integrated choice and latent variable framework. The study accounts for day-to-day variability in commuting behavior, also known as multimodality, by modeling the weekly frequency of commuting by different travel modes instead of modeling choices for a single trip/day. Using stated preference data collected in the Spring of Academic Year 2016–2017, the models are applied to a case study of students who are highly dependent on private cars at the American University of Beirut (AUB), Lebanon. Policy analysis is conducted to investigate the impact of different price levels and modal attributes on the students’ mode choice behavior. Under practical scenarios, results show that more than 55% of students would adopt a multimodal travel behavior in a given week and that 9–20% of trips are expected to be made by shared-taxi and 12–25% by shuttle. Thus, modeling single trip/day choices instead of weekly decisions would lead to limitations in model forecasts related to the full impact of the proposed policies over longer periods. Results also show that the full enumeration model guarantees higher prediction accuracy and results in an estimate of value of time that is closer to other local estimates for the study area.