Ride-sourcing platforms, among other solution services, offer convenience and flexibility when it comes to pick-up/drop-off time and location. Similarly, ride-splitting renders itself as an extension of ride-sourcing where platform users agree to share their rides in return for a reduced fare yet possibly a longer travel time. Despite the numerous advantages that sharing introduced to the platform operator by reducing the fleet size necessary to serve demand levels, e-hailing is still overall negatively impacting traffic performance in urban spaces. This is partially due to the current tendency of users to favor solo over shared rides. This paper aims to use aggregate traffic flow models to put forward a network space redistribution policy that has the potential to reduce total delays of the different mode users in the network. Accordingly, we investigate the solo-pool demand split that minimizes the total Passenger Hours Traveled for all network commuters in the event where shared rides are allowed to use underutilized bus lanes. As a result, the choice to share is associated with an inevitable additional detour distance but with a lower-than-expected trip time compared to standard scenarios where the whole fleet utilizes the same network space. In this paper, we present an analytical macroscopic modeling approach to evaluate equilibrium solutions between network supply and multi-modal demand. By resorting to a numerical example of the model, we show that the optimal strategy that minimizes delays for multi-modal transport users occurs when only a fraction of the pooling vehicles uses the dedicated bus lanes. This fraction is dependent on the distribution of space and the value of demand for private vehicles, buses, and ride-hailing services.