  We here investigate static, spherically symmetric solutions to
$\mathfrak{su}(\infty)$ Einstein-Yang-Mills theory with a negative cosmological
constant $\Lambda$ in the case of dyonic solutions, which possess a non-trivial
electric sector of the gauge field. We are able to find non-trivial solutions
to this system, and show that some may be uniquely characterised by a countably
infinite set of global charges, which may have implications for Bizon's
modified `No Hair' theorem.
