The code requires that you keep the existing cleanout the same diameter.
I have attached an illustrated solution where you can attach your new line to the cleanout while maintaining the cleanout to code spec.
Note the length limits on the top horizontal line. If your horizontal run is equal to or less than the defined lengths you will not need to install the studor vent.
The vertical length is not critical unless it exceeds 40' then you would need to increase the line by one nominal trade size (1-1/2" to 2")
You would need to know whether your local code is based upon either the Uniform Plumbing Code or the International Residential Code.
