Point clouds have been recently used in applications involving real-time capture and rendering of 3D objects. In a point cloud, for practical reasons, each point or voxel is usually associated with one single color along with other attributes. The region-adaptive hierarchical transform (RAHT) coder has been proposed for single-color point clouds. The cloud is usually captured by many cameras and the colors are averaged in some fashion to yield the point color. This approach may not be very realistic since, in real world objects, the reflected light may significantly change with the viewing angle, especially if specular surfaces are present. For that, we are interested in a more complete representation, the plenoptic point cloud, wherein every point has associated colors in all directions. Here, we propose a compression method for such a representation. Instead of encoding a continuous function, since there is only a finite number of cameras, it makes sense to compress as many colors per voxel as cameras, and to leave any intermediary color rendering interpolation to the decoder. Hence, each voxel is associated with a vector of color values, for each color component. We have here developed and evaluated four methods to expand the RAHT coder to encompass the multiple colors case. Experiments with synthetic data helped us to correlate specularity with the compression, since object specularity, at a given point in space, directly affects color disparity among the cameras, impacting the coder performance. Simulations were carried out using natural (captured) data and results are presented as rate-distortion curves that show that a combination of Kahunen-Loève transform and RAHT achieves the best performance.