  We investigate multi-monopole solutions of a modified version of the BPS
Yang-Mills-Higgs model in which a term quartic in the covariant derivatives of
the Higgs field (a Skyrme term) is included in the Lagrangian. Using numerical
methods we find that this modification leads to multi-monopole bound states. We
compute axially symmetric monopoles up to charge five and also monopoles with
Platonic symmetry for charges three, four and five. The numerical evidence
suggests that, in contrast to Skyrmions, the minimal energy Skyrmed monopoles
are axially symmetric.
