  Work of Grantcharov et al. develops a theory of abstract crystals for the
queer Lie superalgebra $\mathfrak{q}_n$. Such $\mathfrak{q}_n$-crystals form a
monoidal category in which the connected normal objects have unique highest
weight elements and characters that are Schur $P$-polynomials. This article
studies a modified form of this category, whose connected normal objects again
have unique highest weight elements but now possess characters that are Schur
$Q$-polynomials. The crystals in this category have some interesting features
not present for ordinary $\mathfrak{q}_n$-crystals. For example, there is an
extra crystal operator, a different tensor product, and an action of the
hyperoctahedral group exchanging highest and lowest weight elements. There are
natural examples of $\mathfrak{q}_n$-crystal structures on certain families of
shifted tableaux and factorized reduced words. We describe extended forms of
these structures that give similar examples in our new category.
