This study models a multi-modal network with ridesharing services. The developed model reproduces the scenario where travelers with their own cars may choose to be a solo-driver, a ridesharing driver, a ridesharing rider, or a public transit passenger while travelers without their own cars can only choose to be either a ridesharing rider or a public transit passenger. The developed model can capture the (clock) time-dependent choices of travelers and the evolution of traffic conditions, i.e., the within-day traffic dynamics. In particular, the within-day traffic dynamics in a city region is modeled through an aggregate traffic representation, i.e., the Macroscopic Fundamental Diagram (MFD). This paper further develops a doubly dynamical system that examines how the within-day time-dependent travelers’ choices and traffic conditions will evolve from day to day, i.e., the day-to-day dynamics. Based on the doubly dynamical framework, this paper proposes two different congestion pricing schemes that aim to reduce network congestion and improve traffic efficiency. One scheme is to price all vehicles including both solo-driving and ridesharing vehicles (for ridesharing trips, the price is shared by the driver and rider), while the other scheme prices the solo-driving vehicles only in order to encourage ridesharing. The pricing levels (under each scheme) can be determined either through an adaptive adjustment mechanism from period to period driven by observed traffic conditions, or through solving a bi-level optimization problem. Numerical studies are conducted to illustrate the models and effectiveness of the pricing schemes. The results indicate that the emerging ridesharing platform may not necessarily reduce traffic congestion, but the proposed congestion pricing schemes can effectively reduce congestion and improve system performance. While pricing solo-driving vehicles only may encourage ridesharing, it can be less effective in reducing the overall congestion when compared to pricing both solo-driving and ridesharing vehicles.