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In PFS my character has access to an alternate version of an Elixir of Dragon's Breath that does more damage and has a higher caster level (CL 10 instead of CL 7 for the standard version) but this alternate version doesn't mention what the save DC is. Does it remain the DC 16 of the standard version or increase?
Yes, it stays.
Save DC of items is equal to 10 + Spell level + modifier of minimum casting stat to cast the spell. Caster level has nothing to do with that equation.