  We study some special features of $F_{24}$, the holomorphic $c=12$
superconformal field theory (SCFT) given by 24 chiral free fermions. We
construct eight different Lie superalgebras of "physical" states of a chiral
superstring compactified on $F_{24}$, and we prove that they all have the
structure of Borcherds-Kac-Moody superalgebras. This produces a family of new
examples of such superalgebras. The models depend on the choice of an
$\mathcal{N}=1$ supercurrent on $F_{24}$, with the admissible choices labeled
by the semisimple Lie algebras of dimension 24. We also discuss how $F_{24}$,
with any such choice of supercurrent, can be obtained via orbifolding from
another distinguished $c=12$ holomorphic SCFT, the $\mathcal{N}=1$
supersymmetric version of the chiral CFT based on the $E_8$ lattice.
