  The chiral algebra of the symmetric product orbifold of a single-boson CFT
corresponds to a "higher spin square" algebra in the large $N$ limit. In this
note, we show that a symmetrized collection of $N$ bosons defines a similar
structure that we refer to as the higher spin rectangle algebra. We explore the
relation of this algebra to the higher spin square algebra. The existence of
such a truncated algebra hints at bulk theories interpolating between Vasiliev
higher spin theory and string theory.
