The million degree plasma of the solar corona must be supplied by the underlying layers of the atmosphere. The mechanism and location of energy release, and the precise source of coronal plasma, remain unresolved. In earlier work we pursued the idea that warm plasma is supplied to the corona via direct heating of the chromosphere by nanoflares, contrary to the prevailing belief that the corona is heated in-situ and the chromosphere is subsequently energized and ablated by thermal conduction. We found that single (low-frequency) chromospheric nanoflares could not explain the observed intensities, Doppler-shifts, and red/blue asymmetries in Fe XII and XIV emission lines. In the present work we follow up on another suggestion that the corona could be powered by chromospheric nanoflares that repeat on a timescale substantially shorter than the cooling/draining timescale. That is, a single magnetic strand is re-supplied with coronal plasma before the existing plasma has time to cool and drain. We perform a series of hydrodynamic experiments and predict the Fe XII and XIV line intensities, Doppler-shifts, and red/blue asymmetries. We find that our predicted quantities disagree dramatically with observations and fully developed loop structures cannot be created by intermediate- or high-frequency chromospheric nanoflares. We conclude that the mechanism ultimately responsible for producing coronal plasma operates above the chromosphere, but this does not preclude the possibility of a similar mechanism powering the chromosphere; extreme examples of which may be responsible for heating chromospheric plasma to transition region temperatures (e.g. type II spicules).