This paper investigates a two-parameter extension of the Λs CDM model, along with the Λ CDM model, by allowing variations in the effective number of neutrino species (Neff) and their total mass (Σmν). The motivation is to determine whether the Λs CDM framework can address major cosmological tensions without deviating from the standard model of particle physics. The extended Λs CDM model, referred to as Λs CDM+Neff+Σmν, is analyzed using Planck, BAO, and BAOtr datasets. The results show that the model does not exhibit significant tension when considering Planck-alone data. However, incorporating BAO data limits the success of the Λs CDM extension. The weakly model-dependent BAOtr data, along with Planck and Planck+PP&SH0ES, favor an H0 value of approximately 73 km s⁻¹ Mpc⁻¹, consistent with local measurements. In cases where BAOtr is part of the combined dataset, the mirror AdS-dS transition is effective in providing enhanced H0 values, and the model remains consistent with the standard model of particle physics. Both the H0 and s8 tensions are effectively addressed, with some compromise in the case of the Planck+BAO dataset. The upper bounds on Σmν are fully compatible with neutrino oscillation experiments. The findings suggest that late-time physics beyond Λ CDM, such as Λs CDM, can suffice to alleviate major cosmological tensions without altering the standard description of the pre-recombination universe.This paper investigates a two-parameter extension of the Λs CDM model, along with the Λ CDM model, by allowing variations in the effective number of neutrino species (Neff) and their total mass (Σmν). The motivation is to determine whether the Λs CDM framework can address major cosmological tensions without deviating from the standard model of particle physics. The extended Λs CDM model, referred to as Λs CDM+Neff+Σmν, is analyzed using Planck, BAO, and BAOtr datasets. The results show that the model does not exhibit significant tension when considering Planck-alone data. However, incorporating BAO data limits the success of the Λs CDM extension. The weakly model-dependent BAOtr data, along with Planck and Planck+PP&SH0ES, favor an H0 value of approximately 73 km s⁻¹ Mpc⁻¹, consistent with local measurements. In cases where BAOtr is part of the combined dataset, the mirror AdS-dS transition is effective in providing enhanced H0 values, and the model remains consistent with the standard model of particle physics. Both the H0 and s8 tensions are effectively addressed, with some compromise in the case of the Planck+BAO dataset. The upper bounds on Σmν are fully compatible with neutrino oscillation experiments. The findings suggest that late-time physics beyond Λ CDM, such as Λs CDM, can suffice to alleviate major cosmological tensions without altering the standard description of the pre-recombination universe.