Can I play Showstopper on an already buffed unit in my base?

Yes, you can play Showstopper on a unit in your base that is already buffed.

According to RiftJudge FAQ #3683 and Rule 426.1.c, playing Showstopper on a unit that is already buffed remains a legal play. When the spell resolves, the unit will not receive an additional buff, but all other effects of the card—specifically moving the unit to a battlefield—will still resolve normally.