You will void your motor oil warranty. No lube oil manufacturer will warranty their product if it's chemistry may have been altered by the introduction of some other company's additive. If you lose your engine because of a lube failure, you'll be on your own.
You might harm your engine. We were taught to not recommend high ZDDP (~2000 ppm) racing oils for street engines, because they could cause pitting or spalling if left in your engine for extended periods. Those oils we sold were formulated for boosted nitro or alcohol engines, which have their own unique lube needs.
What will you gain? Will it actually work in concert with the additive already in your oil? Will you have enough, too much, or too little? You can't really know the answer to any of these questions. Figure out what you need, and buy a product that already that amount in it. They're out there. You just might not be able to walk in the local parts store and get some off the shelf.