AFAIAA, unlike a bus there is no limit for the number of people allowed on a train. I've driven a train that was so full it stalled halfway up a hill. Fortunately a reboot brought it back to life and it struggled to the top.
Although a severely crowded train train doesn't cause a big worry for the TOCs, seriously crowded platforms do. There will come a point where the station staff close off the barriers/gatelines to prevent anymore customers enterring the station. This happens regularly at London Victoria where a beeping alarm warns passengers coming off Southern & Southeastern platforms that the LUL entrances are being temporarily closed due to overcrowding down on the tube platforms. Most passengers are used to it and just wait patiently - it's part of living on an overcrowded island.
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