Though visible-light communication (VLC) channels are contained by opaque boundaries, they present unique challenges in the development of multi-user/multi-cell scenarios. In this paper, two hybrid transmission schemes are proposed for managing multiple users in multi-cell VLC networks. The proposed schemes are based on using non-orthogonal multiple access (NOMA) in the network access points (APs), while applying zero-forcing (ZF) pre-coding to the cell edge users' signals, which are cooperatively broadcast from the APs. The proposed approach allows a reduction of the inter-cell interference affecting the cell-edge users thanks to ZF pre-coding, while dealing with inter-user interference for cell-center users via NOMA signaling. Considering different transmission scenarios, we show the improvement in the network total achievable data rate as well as fairness, as compared to conventional NOMA. For example, for a typical scenario considered, an improvement of up to 39% in total achievable rate and up to 112% in the network fairness is achieved. The proposed approach also presents a clear advantage over the conventional ZF pre-coding, for which the maximum number of users is constrained to the number of APs.