Sustainable housing provision through vertical extension - a thread

The housing crisis means that 1 in 200 people in England are now homeless, with more than 90% of these living in temporary accommodation. Poor historic housing provision and failure to meet targets has also meant that the average cost of a first time home in the UK is now ~£200k.
As buildings are responsible for ~40% of global carbon emissions, with the construction sector contributing also 62% of the UK's waste, it is clear that future housing provision *must* be more sustainable if we are to limit global warming to 1.5°C.
One way that we can work towards this is through the vertical extension of our existing buildings - providing new usable floorspace whilst consuming fewer resources (and land!), and generating less waste than through demolition/reconstruction.
This will also hold back urban sprawl and promote high density, mixed-use spaces within our cities - something that is thought to make us more productive, and means that we need less infrastructure to support more people!