The paper *Classification of metaplectic modular categories* by Ardonne-Cheng-Rowell-Wang (2016) mentions (in Section 3) the Grothendieck ring for the metaplectic modular categories, i.e. $SO(N)_2$, $N>1$ odd (see below).

Now by exchanging $1$ and $Z$ in lines (2) and (3), we get a new family of fusion rings.

**Question 1**: Are there (unitary) fusion categories corresponding to this new family?

(which could be called *twisted metaplectic*)

**Question 2**: Can this procedure be extended to other fusion categories?

There is a way to make two new families: in the right hand-side of (2) and (3), put $$\oplus (X_1 \oplus X_2)^{\oplus \frac{N-1}{2}}$$ By this modification, you still have a fusion ring, but the objects $X_1, X_2$ are now of FPdim $N$. Again you have the usual and the twisted version. Note that after this modification, the usual case with $N=3$ corresponds to the Grothendieck ring of $\mathrm{Rep}(S_4)$.

**Bonus question 1**: Are there (unitary) fusion categories corresponding to these new families?

**Bonus question 2**: Can this procedure be extended to other fusion categories?