Detecting and characterizing nanoscale material properties and functionalities of samples and emerging devices is of rapidly growing interest in nano- and bio-technologies. We introduce a new inner-paddled cantilever design that can circumvent the limitations of a conventional AFM cantilever, in a new two-field design. The inner-paddle provides an additional, independent pathway to respond to variations of material properties. In the context of functional imaging techniques such as PFM and AFM-IR, the two-transduction channels can resolve the long-time issue of crosstalk between surface topography and material functionality from which a conventional AFM cantilever has inherently suffered. Moreover, when this new cantilever system is tested in tapping mode AFM, the inner-paddle can amplify a higher harmonic that coincides precisely with a higher vibration mode, resulting in multi-frequency AFM for compositional mapping. This is the result of internal resonance between the fundamental bending beam mode and a higher mode. Unlike other multi-frequency AFM techniques, the input signal contains only a single frequency, yet the cantilever response contains two frequencies with large signal-to-noise ratios (SNR). This is yet one more example of intentional use of strong nonlinearity for design.