One of the main challenges in the field of thermal radiation is to actively control the near-field radiative heat transfer (NFRHT) between closely spaced bodies. In this context, the use of an external magnetic field has emerged as a very attractive possibility and a plethora of physical phenomena have been put forward in the last few years. Here, we predict some additional magnetic-field-induced phenomena that can take place in the context of NFRHT between planar layered structures containing magneto-optical (MO) materials (mainly doped semiconductors like InSb). In particular, we predict the possibility of increasing the NFRHT upon applying an external magnetic field in an asymmetric structure consisting of two infinite plates made of InSb and Au. We also study the impact of a magnetic field in the NFRHT between structures containing MO thin films and show that the effect is more drastic than in their bulk counterparts. Finally, we systematically investigate the anisotropic thermal magnetoresistance, i.e., the dependence of the radiative heat conductance on the orientation of an external magnetic field, in the case of two infinite plates made of InSb and show that one can strongly modulate the NFRHT by simply changing the orientation of the magnetic field. All the phenomena predicted in this work can be experimentally tested with existent technology and provide new insight into the topic of active control of NFRHT.