The techniques developed in the paper can potentially be extended to LO coloring of hypergraphs beyond the 3-uniform case. The key lies in adapting the SDP-based rounding methods and combinatorial tools to suit the specific structure and requirements of higher-order hypergraphs. By understanding the underlying principles of LO coloring and the SDP relaxation used in the paper, researchers can explore how to generalize these techniques to hypergraphs with different uniformity levels. This extension may involve modifying the algorithms to account for the increased complexity and connectivity present in higher-order hypergraphs. Additionally, considering the unique properties of hypergraphs beyond the 3-uniform case will be crucial in designing efficient and effective coloring algorithms for such scenarios.