Well, if you want to cut deep, there are several things about anatomy which you should take into considderation to not run into probelms which you don't want to face. There are two big blood vessels to be found epifascial (directly under the skin) on the thorax: it:s the vena Vena epigastrica superficiales and it's branches and the Vena thoraca epigastrica with it's branches. Better check on where they run before hurting them, as this might be life threatening.
The second issue is that small lymphatic vessels (also within the skin) and nerves are running in a transversal direction on the throax, which means that you should also do transversal cuts to hurt as few as possible of them.

Probably you have already knowh all this, but it is better when to heaer it a thousend times then not knowing it at all.


(Cutting deep is basically not to be recommended according to my opinion!)