No single food/elixir may provide more than one buff. Further, when a food/elixir buff timer begins, it overwrites any existing buff timer Link was enjoying. Thus, food/elixir buffs aren't stackable with other food/elixir buffs (but they can be combined with armor buffs; see below).

Do potion effects stack in Botw?

Effects don't stack. Extra hearts aren't an effect. Extra stamina also isn't an effect.

Can you have multiple effects at once in Botw?

Yes. At any given time you can have both extra hearts and stamina, 1 stat boost (attack or defense) and 1 temperature (cold or heat) buff.