Venting Through an Outside Wall

I have added a second bathroom to the 2nd level of a two story house.

The shower and tub are on the main stack, however the toilet and sink are not in an area where I can join onto that stack.

The toilet is beside an outside wall.

Is it possible to:

1) Run the stack to the outside wall
2) Put the exit put a few feet higher than the toilet

This will save me going all the way up the wall and over to a place on the roof and installing a new vent stack on a brand new roof.

Inspectors like to see the vents extend through the roof.

quote; installing a new vent stack on a brand new roof.

What is the problem with that? WE do it all the time unless it is a new house and the roof is not installed yet.