According to the uniform plumbing code the soil pipe or stack pipe shall extend vertically not less than six 6 inches.
Vent stack height above roof.
Upc i 906 1 and 906 2.
The 6 you describe should be just fine.
In locations known for snow the vent pipe needs to be at least 51 mm 2 in in diameter and 305 mm inside an insulated area of a building before extending through the roof.
Vent pipes shall terminate not less than 6 inches above the roof measured from the highest point where the vent intersects the roof.
Each vent pipe or stack shall extend through its flashing and shall terminate vertically not less than 6 inches 152 mm above the roof nor less than 1 foot 305 mm from a vertical surface.
The size of the stack vent shall be not less than the size of the waste stack.
Vents in these locations also should extend 610 mm 24 in above a roof.
12 4 1 extension above roofs.
Additionally vent pipes must be at least 305 mm 12 in away from a vertical surface.
A stack vent shall be installed for the waste stack.
The slope is about 4 high for every 12 horizontal.
Vent pipes should extend to outdoors above the building roof and should terminate vertically not less than 6 above the roof surface nor more than 24 and must be at least 12 from any vertical surface such as a nearby sidewall.
Quoting the irc model plumbing code.
4 except for a fresh air inlet where a vent pipe is terminated in open air the terminal shall be located a not less than 1 000 mm above or not less than 3 5 m in any other direction from every air inlet openable window or door.
Where a roof is to be used for any purpose other than weather protection the vent extensions shall be run at least seven feet above the roof.
Above the roof plumbing vent height.
Above the roof nor less than one 1 foot.
Plumbing code citations for plumbing vent or vent stack clearance distances.
A vent stack is not like a chimney which requires 2 higher than any roof within 10.
You are letting air into the plumbing system of the house.
Offsets shall be permitted in the stack vent and shall be located at least 6 inches 152 mm above the flood level of the highest fixture and shall be in accordance with section p3104 5.
D where the buildingis 4 storeys or less in height the vent pipe terminates above the roof of the building.
I d maybe try to tie that existing 2 vent into your new 3.