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Whilst running late yesterday, I pondered this question:
How many times is it possible to leave a train and rejoin the same one at a later station on its trip?

I've certainly managed it once, (Hammersmith, Barons Court, South Kensington) and I think it's possible to do it at least 5 times, along the District line Upminster-Ealing, although I've not checked the timings.

If this could be worked into an R15 alternative challenge, then it may be interesting.

The Circle line. Many. Many. Times.

Bakerloo along the Watford DC stretch, Jubilee/Metropolitan (Baker Street-Wembley Park), Piccadilly/Victoria (FPK-KGX-GPK), Piccadilly-Metropolitan (Rayners Lane-King's Cross), Northern/Victoria (Stockwell-Warren Street/Euston), District/H&C on the c2c section, even possibly Metropolitan against Chiltern.