What impact would introducing 15 times more soy worldwide do to the price of soy?
Roberts and Schlenker (2013) estimate the price elasticity of demand for agricultural commodities to be about -0.08 to -0.05. These are elasticities estimated over much smaller changes in $p$ and $q$ than you are suggesting. Remember that the elasticity is effectively percent change in $q$ for a percent change in $p$, so we can ask what the percent change in $p$ is for a percent change in $q$. 

If production is 15x more soy than there is currently (in total, so globally) then this is a 1500% ((1*15+1 - 1)/1) increase in soy. Using the high end (most elastic), we get that prices have to fall 18,750% (15/-0.08) to clear the market at this new higher quantity. This is impossible, so this tells us that our local elasticity measures won't do to solve this problem. It also suggests that there would be no reason to add so much soy bean production, because demand is likely unable to handle so much soy.