  Let $G$ be a nonabelian group. We show how a collection of compatible
endomorphisms $\psi_i:G\to G$ such that $\psi_i([G,G])\le Z(G)$ for all $i$
allows us to construct a family of bi-skew braces called a brace block. We
relate this construction to other brace block constructions and interpret our
results in terms of Hopf-Galois structures on Galois extensions. We give
special consideration to the case where $G$ is of nilpotency class two, and we
provide several examples, including finding the maximal brace block containing
the group of quaternions.
