I think this question has been asked before but I can't quite find exactly my situation.
I'm pretty sure this isn't to code, either, except the IPC code section 905.2 apparently says
All vent and branch vent pipes shall be so graded and connected as to drain back to the drainage pipe by gravity.
which this arrangement arguably does have.
I have a bathroom in an old (1928) home. I am gutting it and I want to reuse the existing stack vent. But I'm replacing all other plumbing, including the main part of the stack. I was going to cut the old stack at the bottom of the vent and guide the new stack into the old vent.
Old stack is 4" cast iron. So is the old stack vent.
The new shower drain and toilet will use the stack vent directly.
However, to make use of the old vent for the sink, which is going to be on the opposite wall to the old vent stack, I'd have to route the vent pipe up and over the steep roof gable, and back down.
I think the answer is going to be "create a new vent for the sink and poke it through the roof" -- and I'm ok with that. But I did just get this roof replaced 3 years ago and I'd hate to poke a hole in it if I didn't have to.
Images for clarity
Old vent stack -- black cast iron going up and to the left.
Proposed vent including question area (in dashed red oval)
Detail showing the steepness of the roof angle