= Solution
Write $J_k(\lambda)$ for the <Jordan block> with diagonal $\lambda$ and ones on the superdiagonal. Its <characteristic polynomial> and <minimal polynomial> are both $(x-\lambda)^k$. Therefore one answer to the first request is
$$
\boxed{M=J_3(2)\oplus J_2(-1)}.
$$
For the second request, take
$$
\boxed{M_1=J_2(3)\oplus J_2(3)\oplus J_1(3)\oplus J_2(1)},
$$
$$
\boxed{M_2=J_2(3)\oplus J_1(3)\oplus J_1(3)\oplus J_1(3)\oplus J_2(1)}.
$$
The algebraic multiplicities are five and two, and the largest block at each <eigenvalue> has size two, so both prescribed <polynomials> hold. They are not <similar matrices>: the <eigenspace> at three has dimensions three and four respectively, and similarity preserves <eigenspace> dimension.
\b[There is no third similarity class.] At <eigenvalue> one, the total size two and maximal block size two force the single block $J_2(1)$. At <eigenvalue> three, the blocks partition five, each has size at most two, and at least one has size two. The only partitions are $2+2+1$ and $2+1+1+1$. The uniqueness of <Jordan normal form> up to block order therefore leaves exactly the two classes already exhibited.
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