There is some confusion here, the District line (then District Railway) initially wanted to extend its line from Hounslow. The line ended at a bridge abutment facing south (its long gone, Hounslow bus garage is now on the site). The station being replaced by current Hounslow East on a later line (now used by Piccadilly line to Heathrow)
It would have headed towards Whitton (near where Twickenham Rugby stadium is nowadays), crossed the LSWR line and joined the line towards Kingston near Strawberry Hill. But at the time District Railway was skint and couldn't afford it, and was some local objections.
The District Railway later tried to get extensions beyond Wimbledon, but would have required parallel tracks. Ultimately they didn't want to (or couldn't afford to) contribute to the widening. The LSWR did a lot of work towards the 6 tracking from about 1910 until work fizzled out during WW1 in 1915. Lots of bridges from Clapham Cutting to Hampton Court junction were rebuilt and have room for the 6 tracks, although some bits of the extra trackbed have been blocked by signalling, new structures and cable runs in more recent years. Which is why now expensive to finish the widening and Crossrail 2 isn't able to use much of the previously cleared space.
The LSWR added 4 rail electrification for District from Putney to Wimbledon (and Hammersmith-Richmond) around 1904. Electrified Kingston loop and to Hampton Court /Claygate in 1916, but electrification didn't get beyond Claygate on Guildford new line until 1925
The District did later look at extensions beyond Wimbledon, but it all ended in a big agreement with then new Southern Railway that District wouldn't expand beyond Wimbledon, Northern line expansion wouldn't go beyond Morden and Wimbledon and Sutton line would be built.
The other new line was the Leatherhead loop, opened to Tolworth, and extended to Chessington, but WW2 halted it. I believe about another half mile was added during war as sidings. But Green Belt killed remainder. If the wartime section was ever reopened to a new single platform station near Chalky Lane would be very close to Chessington World of Adventures theme park.