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With the increasing sensitivities of the gravitational wave (GW) detectorsand more detectors joining the international network, the chances of detectionof a stochastic GW background (SGWB) are progressively increasing. Differentastrophysical and cosmological processes are likely to give rise to backgroundswith distinct spectral signatures and distributions on the sky. The observedSGWB will therefore be a superposition of these components. Hence, one of thefirst questions that will come up after the first detection of a SGWB willlikely be about identifying the dominant components and their distributions onthe sky. Both these questions were addressed separately in the literature,namely, how to separate components of isotropic backgrounds and how to probethe anisotropy of a single component. Here, we address the question of how toseparate distinct anisotropic backgrounds with (sufficiently) differentspectral shapes. We first obtain the combined Fisher information matrix fromfolded data using an efficient analysis pipeline PyStoch, which incorporatescovariances between pixels and spectral indices. This is necessary forestimating the detection statistic and setting upper limits. However, based ona recent study, we ignore the pixel-to-pixel noise covariance that does nothave a significant effect on the results at the present sensitivity levels ofthe detectors. We show that the joint analysis accurately separates andestimates backgrounds with different spectral shapes and different skydistributions with no major bias. This does come at the cost of increasedvariance. Thus making the joint upper limits safer, though less strict than theindividual analysis. We finally set joint upper limits on the multicomponentanisotropic background using Advanced LIGO data taken up to the first half ofthe third observing run.

Jointly setting upper limits on multiple components of an anisotropic stochastic gravitational-wave background