In 1960, Charles Stein conjectured that the best invariant estimate of a single co-ordinate of a $p$-dimensional location parameter would be admissible if $p \leqq 3$ but inadmissible if $p \geqq 4$. This appear present a class of examples which supports Stein's conjecture.
"Admissibility of the Best Invariant Estimator of One Co-Ordinate of a Location Vector." Ann. Statist. 3 (2) 448 - 450, March, 1975. https://doi.org/10.1214/aos/1176343069