It is always interesting to investigate how well can a future experiment perform with respect to others (present or future ones). Cosmology is really an exciting field where a lot of puzzles are still unknown. In this paper, we consider a generalized dark energy (DE) scenario where anisotropic stress is present. We constrain this generalized cosmic scenario with an aim to investigate how gravitational waves standard sirens (GWSS) may constrain the anisotropic stress, which, according to the standard cosmological probes, remains unconstrained. In order to do this, we generate the luminosity distance measurements from O(103) mock GW events that match the expected sensitivity of the Einstein Telescope. Our analyses report that, first of all, GWSS can give better constraints on various cosmological parameters compared to the usual cosmological probes, but the viscous sound speed appearing due to the DE anisotropic stress is totally unconstrained even after the inclusion of GWSS.