We demonstrate that exposed-core microstructured optical fibers offer multiple degrees of freedom for tailoring third harmonic generation, through core diameter, input polarization, and nanofilm deposition. Varying these parameters allows control of the phase-matching position between an infrared pump wavelength and the generated visible wavelengths. In this work we show how increasing the core diameter over previous experiments (2.57 µm compared to 1.85 µm) allows the generation of multiple wavelengths, which can be further controlled by rotating the input pump polarization and the deposition of dielectric nanofilms. This can lead to highly tailorable light sources for applications such as spectroscopy or nonlinear microscopy.