  In this article, we construct complete embedded constant mean curvature
surfaces in $\mb{R}^3$ with freely prescribed genus and any number of ends
greater than or equal to four. Heuristically, the surfaces are obtained by
resolving finitely many points of tangency between collections of spheres. The
construction relies a family of constant mean curvature surfaces constructed in
\cite{Kleene}, constructed as graphs over catenoidal necks of small scale.
