Many recent works have shown that the angular resolution of ground-based detectors is too poor to characterize the
anisotropies of the stochastic gravitational-wave background (SGWB). For this reason, we asked ourselves if a
constellation of space-based instruments could be more suitable. We consider the Laser Interferometer Space
Antenna (LISA), a constellation of multiple LISA-like clusters, and the Deci-hertz Interferometer Gravitationalwave
Observatory (DECIGO). Specifically, we test whether these detector constellations can probe the anisotropies
of the SGWB. For this scope, we considered the SGWB produced by two astrophysical sources: merging compact
binaries, and a recently proposed scenario for massive black hole seed formation through multiple mergers of
stellar remnants. We find that measuring the angular power spectrum of the SGWB anisotropies is almost
unattainable. However, it turns out that it could be possible to probe the SGWB anisotropies through crosscorrelation
with the cosmic microwave background (CMB) fluctuations. In particular, we find that a constellation
of two LISA-like detectors and CMB-S4 can marginally constrain the cross-correlation between the CMB lensing
convergence and the SGWB produced by the black hole seed formation process. Moreover, we find that DECIGO
can probe the cross-correlation between the CMB lensing and the SGWB from merging compact binaries.
