  We present comprehensive spectroscopic and photometric analyses of the
intermediate luminosity Type Iax supernova (SN Iax) 2019muj based on multi-band
datasets observed through the framework of the OISTER target-of-opportunity
program. SN 2019muj exhibits almost identical characteristics with the
subluminous SNe Iax 2008ha and 2010ae in terms of the observed spectral
features and the light curve evolution at the early phase, except for the peak
luminosity. The long-term observations unveil the flattening light curves at
the late time as seen in a luminous SN Iax 2014dt. This can be explained by the
existence of an inner dense and optically-thick component possibly associated
with a bound white dwarf remnant left behind the explosion. We demonstrate that
the weak deflagration model with a wide range of the explosion parameters can
reproduce the late-phase light curves of other SNe Iax. Therefore, we conclude
that a common explosion mechanism operates for different subclass SNe Iax.
