Image-based relighting (IBRL) renders the appearance of a subject in a novel lighting environment as a linear combination of the images of its reflectance field, the appearance of the subject lit by each incident lighting direction. Traditionally, a tristimulus color camera records the reflectance field as the subject is sequentially illuminated by broad-spectrum white light sources from each direction. Using a multispectral LED sphere and either a tristimulus (RGB) or monochrome camera, we photograph a still life scene to acquire its multispectral reflectance field -- its appearance for every lighting direction for multiple incident illumination spectra. For the tristimulus camera, we demonstrate improved color rendition for IBRL when using the multispectral reflectance field, producing a closer match to the scene's actual appearance in a real-world illumination environment. For the monochrome camera, we also show close visual matches. We additionally propose an efficient method for acquiring such multispectral reflectance fields, augmenting the traditional broad-spectrum lighting basis capture with only a few additional images equal to the desired number of spectral channels. In these additional images, we illuminate the subject by a complete sphere of each available narrow-band LED light source, in our case: red, amber, green, cyan, and blue. From the full-sphere illumination images, we promote the white-light reflectance functions for every direction to multispectral, effectively hallucinating the appearance of the subject under each LED spectrum for each lighting direction. We also use polarization imaging to separate the diffuse and specular components of the reflectance functions, spectrally promoting these components according to different models. We validate that the approximated multispectral reflectance functions closely match those generated by a fully multispectral omnidirectional lighting basis, suggesting a rapid multispectral reflectance field capture method which could be applied for live subjects.