In this article, we introduce a notion of relative mean metric dimension with potential for a factor map \(\pi : (X,d, T)\rightarrow (Y, S)\) between two topological dynamical systems. To link it with ergodic theory, we establish four variational principles in terms of metric entropy of partitions, Shapira’s entropy, Katok’s entropy and Brin–Katok local entropy respectively. Some results on local entropy with respect to a fixed open cover are obtained in the relative case. We also answer an open question raised by Shi (On variational principles for metric mean dimension, 2021. arXiv:2101.02610) partially for a very well-partitionable compact metric space, and in general we obtain a variational inequality involving box dimension of the space. Corresponding inner variational principles given an invariant measure of (Y, S) are also investigated.