Optical wireless communication (OWC) has recently received massive interest as a new technology that can support the enormous data traffic increasing on daily basis. In particular, laser-based OWC networks can provide terabits per second (Tbps) aggregate data rates. However, the emerging OWC networks require a high number of optical access points (APs), each AP corresponding to an optical cell, to provide uniform coverage for multiple users. Therefore, inter-cell interference (ICI) and multi-user interference (MUI) are crucial issues that must be managed efficiently to provide high spectral efficiency. In radio frequency (RF) networks, rate splitting (RS) is proposed as a transmission scheme to serve multiple users simultaneously following a certain strategy. It was shown that RS provides high data rates compared to orthogonal and non-orthogonal interference management schemes. Considering the high density of OWC networks, the application of RS within each optical cell might not be practical due to severe ICI. In this paper, a novel strategy is derived, referred to as blind interference alignment-rate splitting (BIA-RS), to fully coordinate the transmission among the optical APs, while determining the precoding matrices of multiple groups of users formed beforehand. Therefore, RS can be implemented within each group to manage MUI. The proposed BIA-RS scheme requires two layers of power allocation to achieve high performance. Given that, a max-min fractional optimization problem is formulated to optimally distribute the power budget among the groups and the messages intended to the users of each group. Finally, a power allocation algorithm is designed with multiple Lagrangian multipliers to provide practical and sub-optimal solutions. The results show the high performance of the proposed scheme compared to other counterpart schemes.