The introduction of on-demand ride-hailing platforms totally changed the way people commute. In recent years, several firms entered this market to directly compete with traditional taxi companies. Some of these online platforms offer a carpooling service in which several passengers heading in the same direction can share a ride by being efficiently matched to an available vehicle. Examples of such services in NYC include uberPOOL, Lyft Line and Via. Recently, some of these platforms decided to engage in a profit sharing contract with one of their competitors by introducing a new hybrid service. For example, on June 6th, 2017, Via officially announced a partnership with an online NYC taxi platform called Curb. This partnership allows riders to order a taxi (from either platform), and share some portion of the trip with other riders by using Via's efficient matching algorithm. Given that these two platforms are competing with each other, this form of partnership is often referred to as coopetition. This paper is motivated by this specific type of coopetition. We propose to model the problem using a Multinomial Logit (MNL) choice model, and we characterize the equilibrium outcome. Then, we analyze the impact of introducing the new joint service to the market. Interestingly, we show that a properly designed profit sharing contract will benefit both platforms. This result admits a similar win-win outcome as in the supply chain risk sharing contracts literature, even though these two settings are very different. In addition, we show that one can design such a profit sharing contract that will also benefit the drivers and the riders. Consequently, such a coopetition partnership may benefit every single party (riders, drivers and both platforms).