AFAIR the first upgrade is to level 10, and the second up to whatever the skill's maximum is (13-15).
Ah okay. I was thinking there were three separate upgrades. I had thought maybe the initial starting platforms *were* the first upgrade, but there was never a point where my skill cap was 7, so that's what confused me. It was 5, and then speaking to Hermosa allowed it to be 10 (without even doing her quest yet).