You have to be careful with open brains like lobos, welsos, and such. They do not split like a frogspawn or trumpet, they grow more mouths but often remain attached. Something that affects one portion of it could easily damage the rest. I'm not sure if you can frag them like you can a favia, but if might be worth looking into if it would be a gonner otherwise. lfs might have a saw or something to cut it cleanly.
Based off your description I don't think you are talking about the maze brains or favias, but if you are then yes they do grow more mouths but no they do not split into entirely new heads either. You can cut those along the ridges, avoiding mouths as much as possible since those are likely to die if cut. Fragging is good if you are assuming the coral will die or if you want insurance/a second smaller coral.