Let $S$ be affine. Is there an example of a cokernel in $S$-group schemes, $$A \xrightarrow{\phi} B \to B/\phi(A)$$ which (a) needs to be fppf to be a sheaf, and (b) doesn't have $\mu_d$ as the kernel.

The only examples satisfying (a) that I, and those around me, can come up with are the following:

1. $\mu_{d} \to \mu_{n} \xrightarrow{z \mapsto z^d} \mu_{n/d}$; if $d \notin \mathcal{O}_S^*$
2. $\mu_{d} \to \mathbb{G}_{n} \xrightarrow{z \mapsto z^d} \mathbb{G}_{m}$; if $d \notin \mathcal{O}_S^*$
3. $\mu_{d}(k) \to SL_d(k) \to PGL_d(k)$; if char $k \mid d$

But these feel essentially the same. Are there any different examples?