As nanoscale photonic devices are densely integrated, multiple near-field optical eigenmodes take part in their functionalization. Inevitably, these eigenmodes are highly multiplexed in their spectra and superposed in their spatial distributions, making it extremely difficult for conventional near-field scanning optical microscopy (NSOM) to address individual eigenmodes. Here, we develop a near-field transmission matrix microscopy for mapping the high-order eigenmodes of nanostructures, which are invisible with conventional NSOM. At an excitation wavelength where multiple modes are superposed, we measure the near-field amplitude and phase maps for various far-field illumination angles, from which we construct a fully phase-referenced far- to near-field transmission matrix. By performing the singular value decomposition, we extract orthogonal near-field eigenmodes such as anti-symmetric mode and quadruple mode of multiple nano-slits whose gap size (50 nm) is smaller than the probe aperture (150 nm). Analytic model and numerical mode analysis validated the experimentally observed modes.