We first specialize multiple-scattering theory for uncorrelated distributions of large, low-refracting, absorbing particles to similarly and randomly aligned spheroids. The theory takes into account backscattering interface effects, but neglects the smaller coherent reflection effects. Then we illustrate how the results can be used in optical diagnostics on suspensions of cells for biomedical purposes. We consider the isolation of molecular absorption coefficients for transmission and reflection oximetry on whole blood, scattering-shifted absorption extrema, cell-membrane fragilometry and the effects of osmotic swelling, and some asymmetrical scattering effects for optical monitoring of cell alignment in fluid-transport processes. In measurements on thin samples at wavelengths corresponding to relatively small absorption, pronounced minima in transmission and maxima in reflection have been observed for suspensions about half-full of cells; we discuss simple approximations that indicate the essentials of the phenomena.