You should, I did exactly that sometime ago for only the 5 companies at that time who were super interesting to me. For each of their cover letters I told a pe

You should, I did exactly that sometime ago for only the 5 companies at that time who were super interesting to me. For each of their cover letters I told a personal story that was spot on relevant to the position and their mission/values. It demonstrated all the soft skills....each of them called me within a day or two.