  Tensionless string theory on AdS3 x S3 x T4, as captured by a free symmetric
product orbifold, has a large set of conserved currents which can be usefully
organised in terms of representations of a N=(4,4) supersymmetric higher spin
algebra. In this paper we focus on the single particle currents which generate
the asymptotic stringy symmetry algebra on AdS3, and whose wedge modes describe
the unbroken gauge symmetries of string theory in this background. We show that
this global subalgebra contains two distinct higher spin algebras that generate
the full algebra as a `higher spin square'. The resulting unbroken stringy
symmetry algebra is exponentially larger than the two individual higher spin
algebras.
