Snorter
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There's no mention of them only being allowed one at a time.
PFSRD wrote:
The smite evil effect remains until the target of the smite is dead or the next time the paladin rests and regains her uses of this ability. At 4th level, and at every three levels thereafter, the paladin may smite evil one additional time per day, as indicated on Table: Paladin, to a maximum of seven times per day at 19th level.
They certainly don't stack, that's true.
But there's nothing stopping the paladin blowing the lot on one big fight, or
starting to smite a boss creature (who then escapes), chasing it through it's lair, using a second smite on a minion, then cornering the original boss, still benefitting from the first smite that's still running (as long as it's still the same day).