Deviations of the measured LFU ratios such as 𝑅 𝐷 ( * ) and 𝑅 𝐽/𝜓 from the standard model predictions by 3.3 𝜎 and 1.8 𝜎, respectively, indicate the possible existence of new physics beyond the standard model. Precise measurements of other observables in decays involving 𝑏 → 𝑐ℓ𝜈 ℓ transitions in the future may substantiate or rule out the presence of new physics. Hence, it becomes important to analyze complementary 𝑏 → 𝑐ℓ𝜈 ℓ channels also, such as 𝐵 𝑠 → 𝐷 * * 𝑠 ℓ𝜈 ℓ , where 𝐷 * * 𝑠 = {𝐷 * 𝑠0 , 𝐷 * 𝑠1 , 𝐷 𝑠1 , 𝐷 * 𝑠2 }. The measured ratios 𝑅 𝐷 ( * ) suggest an excess of taus, whereas the measured ratio 𝑅 Λ 𝑐 shows a deficit in taus. The complementary information obtained from the measurement of LFU ratios like 𝑅 𝐷 * * 𝑠 may become crucial in the interpretation of the contributing new physics. In this work, we analyze various 𝑞 2 -dependent observables pertaining to the 𝐵 𝑠 → 𝐷 * * 𝑠 ℓ𝜈 ℓ decay modes within a new physics approach. The new interactions are constrained using available experimental data of 𝑏 → 𝑐ℓ𝜈 ℓ transitions.