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We analyse the full shape of anisotropic clustering measurements from the extended Baryon Oscillation Spectroscopic survey (eBOSS) quasar sample together with the combined galaxy sample from the Baryon Oscillation Spectroscopic Survey (BOSS). We obtain constraints on the cosmological parameters independent of the Hubble parameter $h$ for the extensions of the $Λ$CDM models, focusing on cosmologies with free dark energy equation of state parameter $w$. We combine the clustering constraints with those from the latest CMB data from Planck to obtain joint constraints for these cosmologies for $w$ and the additional extension parameters - its time evolution $w_{\rm{a}}$, the physical curvature density $ω_{K}$ and the neutrino mass sum $\sum m_ν$. Our joint constraints are consistent with flat $Λ$CDM cosmological model within 68\% confidence limits. We demonstrate that the Planck data are able to place tight constraints on the clustering amplitude today, $σ_{12}$, in cosmologies with varying $w$ and present the first constraints for the clustering amplitude for such cosmologies, which is found to be slightly higher than the $Λ$CDM value. Additionally, we show that when we vary $w$ and allow for non-flat cosmologies and the physical curvature density is used, Planck prefers a curved universe at $4σ$ significance, which is $\sim2σ$ higher than when using the relative curvature density $Ω_{\rm{K}}$. Finally, when $w$ is varied freely, clustering provides only a modest improvement (of 0.021 eV) on the upper limit of $\sum m_ν$.