A non-negligible fraction of binary neutron star mergers are expected to form long-lived neutron star remnants, dramatically altering the multimessenger signatures of a merger. Here, we extend existing models for magnetar-driven kilonovae and explore the diversity of kilonovae and kilonova afterglows. Focusing on the role of the (uncertain) magnetic field strength, we study the resulting electromagnetic signatures as a function of the external dipolar and internal toroidal fields. These two parameters govern, respectively, the competition between magnetic-dipole spin-down and gravitational-wave spin-down (due to magnetic-field deformation) of the rapidly rotating remnant. We find that even in the parameter space where gravitational-wave emission is dominant, a kilonova with a magnetar central engine will be significantly brighter than one without an engine, as this parameter space is where more of the spin-down luminosity is thermalized. In contrast, a system with minimal gravitational-wave emission will produce a kilonova that may be difficult to distinguish from ordinary kilonovae unless early epoch observations are available. However, as the bulk of the energy in this parameter space goes into accelerating the ejecta, such a system will produce a brighter kilonova afterglow that will peak in shorter times. To effectively hide the presence of the magnetar from the kilonova and kilonova afterglow, the rotational energy inputted into the ejecta must be less than or similar to 10(-3)to 10(-2)E(rot). We discuss the different diagnostics available to identify magnetar-driven kilonovae in serendipitous observations and draw parallels to other potential magnetar-driven explosions, such as superluminous supernovae and broad-line supernovae Ic.