  The Fermionic linear optical (FLO) extent is a quantity that serves two
roles, firstly it serves as a measure of the "quantumness" (or
non-classicality) of quantum circuits. Secondly it controls the runtime of a
class of classical simulation algorithms, which are state-of-the-art for
simulating quantum circuits formed mostly of FLO unitaries and promoted to
universality by the addition of ``magic states''. It is therefore interesting
to understand the scaling behaviour of the extent as magic states are added to
a circuit. In this work we solve this problem for the case of $4$-qubit parity
eigenstates. We show that the FLO extent of a tensor product of any pure state
and a $4$ qubit parity eigenstate is the product of the extents of the two
tensor factors. Applying this result recursively one proves a conjecture that
the extent is multiplicative for arbitrary tensor products of $4$ qubit magic
states.
