On the possible values of the Rearrangement Number

The rearrangement number $\mathfrak{rr}$ is the least cardinality of a collection of permutations of $\omega$ such that every conditionally convergent real series is disrupted by some permutation in the collection. Blass, Brendle, Brian, Hamkins, Hardy, and Larson proved that $\max\{\operatorname{cov}(\mathcal N),\mathfrak b\}\leq\mathfrak{rr}\leq\operatorname{non}(\mathcal M)$ and asked whether $\mathfrak{rr}<\mathrm{non}(\mathcal M)$ is consistent. We prove that $\mathfrak{rr}<\operatorname{non}(\mathcal M)$ is consistent with ZFC. We also prove, in a different forcing extension, that $\max\{\operatorname{cov}(\mathcal N),\mathfrak b\}<\mathfrak{rr}$. We further derive consequences for the subseries number $\mathfrak{s}_{\mathrm{sub}}$ and the splitting number $\mathfrak s$.