I have come up with a few ideas on how the South London Underground network can be extended.
Hammersmith and City Line Extension - Bromley via Streatham
Hammersmith
Fulham Palace Road (new)
Putney Bridge (int. District)
Wandsworth Town (int. NR)
Earlsfield
Tooting Bec
Streatham
Streatham High street
Upper Norwood
Crystal Palace
Anerley
Kent House
Beckenham Junction
Shortland
Bromley South
Circle Line Extension - Lewisham
Hammersmith
Fulham Palace Road (new)
Putney Bridge (int. District)
Wandsworth Town (int. NR)
Clapham South (int. Northern)
Streatham Hill (new)
Herne Hill (int. NR)
North Dulwich
Peckham Rye Park
Crofton Park
Lewisham
Piccadilly Branch - Barking
Covent Garden
Embankment
Waterloo
Vauxhall
Nine Elms
Battersea Park
Clapham Junction
Wandsworth Common
Balham
Streatham Hill
West Dulwich (int. NR)
Forest Hill (int. NR & ELL)
Catford (int. NR)
Lee (int. NR)
Eltham (int. NR)
Shooters Hill (New)
Woolwich Arsenal (DLR & NR)
Galleons Reach (DLR)
Barking (District, Hammersmith, Overground, NR)
District Line Branch - Wimbledon via Camberwell
Tower Hill
Tower Bridge
Old Kent Road
Camberwell
Stockwell
Wandsworth Road
Clapham Junction
Earlsfield
Southfields
DLR Extension - Bromley via Beckenham
Lewisham
Ladywell
Catford
Lower Sydenham
New Beckenham
Beckenham Junction
Shortlands
Bromley
Metropolitan Line Extension - Sutton, Camberwell and Nunhead Branches
Aldgate
Tower Gateway
Bermonsey
West Branch East Branch
Old Kent Road South Bermonsey
East Dulwich Nunhead
North Dulwich Peckham Rye Park
West Dulwich
West Norwood
Mitcham Common
Sutton
Bakerloo Line Extension - Hayes via Greenwich
Old Kent Road
Queens Road Peckham
New Cross Gate
New Cross
Deptford
Greenwich Observeratory
Blackheath
Lee
Grove Park
Sundridge
Bromley North
Bromley South
Hayes
Northern Line Extension - Swanley via Forest Hill
Kennington
Camberwell
Denmark Hill
East Dulwich
Peckham Rye Park
Honor Oak Park
Catford
Bellingham
Beckenham Hill
Ravensbourne
Bromley
Bickey
St Marys cray
Swanley
East London Line Extension New Cross - Blackheath
New Cross
St Johns
Lewisham
Blackheath
'X' Line Bromley/Swanley - Woolwich/Thamesmere
South East Full Cirle Line Blackheath-Dartford
South East Higher Circle Line
South East Lower Circle Line