Max height of birdcages
TG 20:08 does not give any height to base ratios or maximum heights for external birdcages.
It states that there should be a factor of safety against overturning of at least 1.2.
It would therefore involve working out the wind and instablilty loads on the tubes, boarded lifts, etc against the self weight of the scaffold. Even then the vertical joints will need to be spliced/ lots of ledger, sway and plan bracing would be required.
A tower only has generally four standards and is limited to 8.0m high and should only have a ratio of 3.5 to 1 in lower wind conditions.
Not sure I would want to see a 35m high free standing birdcage only 10.0m wide without additional kentledge, but all depends on wind pressures, location, etc.
Sorry no simple answer as cannot just extrapolate a tower to a birdcage.