Background definitions:

Let $D$ be a triangulated category arising in nature (for instance as the cohomology category of a dg category). An object $E$ in $D$ is called *exceptional* if $RHom(E,E)$ is as simple as possible: quasi-isomorphic to the ground field. A sequence of objects $E_1, E_2,...,E_r$ is called exceptional if each object is exceptional and $RHom(E_i,E_j) \simeq 0$ for $i > j$.

Desired example:

An exceptional collection with either

a) $RHom(E_i,E_j)$ having cohomology in more than one degree for some $i < j$

or

b) some multiplication map $Ext^{m}(E_i,E_j) \otimes Ext^{n}(E_j,E_k) \rightarrow Ext^{m+n}(E_i,E_k)$ that fails to be surjective.

Of course, examples where both a) and b) would be even better.

An ideal example would be of an exceptional triple of vector bundles on a Fano 3-fold or 5-fold satisfying a) and b). But examples coming from representation theory are also welcome.