Directed assembly of particle suspensions in massively parallel formats, such as with magnetic fields, has application in Theological control, smart drug delivery, and active colloidal devices from optical materials to microfluidics. At the heart of these applications lies a control optimization problem for driving the assembly and dissolution of highly monodisperse particle clusters. For magnetic field control, most attention to-date has been centered around in-phase coherent magnetic fields. Instead, we investigate a family of incoherent 3D magnetic fields that are capable of creating controlled and tunable particle assemblies such as dimers, trimers, and quadramers. These field functions can be tuned to assemble monodisperse clusters with long term stability and can quickly switch the clusters between different states. This subset of three-dimensional field functions that we have studied demonstrates the rich phase space available to tune colloidal suspensions with magnetic fields. (C) 2017 Elsevier Inc. All rights reserved.