Can I run a toilet drain on the exterior of my house?
In Illinois this wouldn't be a problem provided it adheres to everything on this list and fits these numbers. Your concern may be that the stack is not a clear vertical run to the roof or that the toilet flange will be more than 24" from it.



My codes expect 4" stacks to begin with. A lot of people seem to get away with 3".


  b) Minimum Size of Building Drain, Horizontal Branches, Drainage Piping
  
  1) The minimum size of any gravity building drain shall be 4 inches in >diameter. 
  -Code