<title>Abstract</title>
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 to 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 late-time flattening light curves as seen in 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 after the explosion. We demonstrate that the weak deflagration model with a wide range of 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.