Most appearances in a Royal Rumble match: Mick Foley - 3
This is one of the most bizarre and enjoyable records in WWE. It's also one that's guaranteed to never be broken.
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In the 1998 Royal Rumble match, Mick Foley appeared three times, once for each of his different monikers - Mankind, Cactus Jack, and Dude Love. No other superstar has appeared twice in the same Royal Rumble match.
Nia Jax sort of came close this year, when she stole R-Truth's spot and entered the men's Royal Rumble match on the same night she competed in the earlier women's Royal Rumble match, but that still consisted of entering two different matches.
Maybe somebody will have multiple personalities that they can enter the Royal Rumble match with. Finn Balor and The Demon come to mind. Even that scenario would still only see him enter the Royal Rumble twice, where he would need to do it two more times to break Foley's record.
Foley was one of the mainstays of the WWE during the attitude era and was known for his hardcore wrestling style. His split personality gimmick was well received by the WWE universe and Foley pulled it off with equal panache.