On the possible values of the Rearrangement Number

The rearrangement number $\mathfrak{r}\mathfrak{r}$ 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 $\max \{\mathrm{cov}(\mathcal{N}),\mathfrak{b}\}\le \mathfrak{r}\mathfrak{r}\le \mathrm{non}(\mathcal{M})$ and asked whether $\mathfrak{r}\mathfrak{r}<\mathrm{n}\mathrm{o}\mathrm{n}(\mathcal{M})$ is consistent. We prove that $\mathfrak{r}\mathfrak{r}<\mathrm{non}(\mathcal{M})$ is consistent with ZFC. We also prove, in a different forcing extension, that $\max \{\mathrm{cov}(\mathcal{N}),\mathfrak{b}\}<\mathfrak{r}\mathfrak{r}$. We further derive consequences for the subseries number ${\mathfrak{s}}_{\mathrm{s}\mathrm{u}\mathrm{b}}$ and the splitting number $\mathfrak{s}$.