I assume you mean without stopping for more than a few minutes to fill your water, get food, use the facilities and such. On that basis, I've done what most rando riders have done, 400k in a day (sometimes as part of a 600k or 1000k multi-day ride).
I'd like to shoot for 400 miles in a day next year, but it's still a lofty goal for the moment.
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Campione Del Mondo Immaginario