There were two quirks. All for One's brother had a quirk that could grant itself to others, which he was not aware of. AFO stole a quirk that allows people to accumulate strength without losing it, and gave it to his brother out of pity. The self-transfer quirk and the strength quirk merged together and became One for All, a single quirk.
One for All is two quirks which have been merged into one single quirk, which can transfer itself, like how All for One can transfer other quirks between people. The original owners were brothers, remember?
So One for All cannot transfer the native quirks that any of its users have. It can transfer only itself, and coexists with the other quirk(s) of its user. Think of how the Noumus has multiple quirks which exist simultaneously.