We have recently suggested that suitably designed plasmonic layers may cloak a given object simultaneously at multiple frequencies (Alù and Engheta 2008 Phys. Rev. Lett. 100 113901). Here, we extend our theory and fully analyze this possibility, highlighting the potentials of this plasmonic cloaking technique and its fundamental limitations dictated by the passivity and causality of the materials involved. The cloaking mechanism relies on the scattering cancellation properties of plasmonic materials. By exploiting their inherent frequency dispersion, it is possible to reduce the 'visibility' of a given object by several orders of magnitude simultaneously at multiple frequencies, such that any of the particular layers composing the cloak is responsible for noticeable reduction of scattering at each frequency of operation.