An extension of Strawderman's results yields minimax admissible estimates for the mean of a $p$-variate normal distribution where the known nonsingular covariance matrix is not necessarily the identity and $p > 2$. Minimax estimators for the case where the covariance matrix is unknown are also given.
"Minimax Estimators of the Mean of a Multivariate Normal Distribution." Ann. Statist. 3 (1) 209 - 218, January, 1975. https://doi.org/10.1214/aos/1176343009