Is there any way to predict the TM mode of a microstrip patch antenna just by looking at its geoetry?Can we guess which TM modes will be present for that antenna?
Yes. The antenna's size will dictate which modes can be supported. Since the patch can be modelled as a resonant cavity, standard equations apply. See for example here.
The actual modes present will be a combination of the supported modes and the feeding mechanism. If you know the field profile of each mode (which we do), you can make a reasonable guess as to which will be excited.