No, they will not.
Supernatural Abilities (Su) wrote:
Supernatural abilities are magical but not spell-like.
There's also an FAQ clarifying that no effects that increase size stack, whether magical or not.
Size increases and effective size increases: How does damage work if I have various effects that change my actual size, my effective size, and my damage dice? wrote:
As per the rules on size changes, size changes do not stack, so if you have multiple size changing effects (for instance an effect that increases your size by one step and another that increases your size by two steps), only the largest applies. The same is true of effective size increases (which includes “deal damage as if they were one size category larger than they actually are,” “your damage die type increases by one step,” and similar language). They don’t stack with each other, just take the biggest one. However, you can have one of each and they do work together (for example, enlarge person increasing your actual size to Large and a bashing shield increasing your shield’s effective size by two steps, for a total of 2d6 damage).
