Maximal cliques in a multipartite graph - efficient?
A maximal clique and a maximum clique are in general different. A set of vertices $S$ is a maximal clique if $S$ is a clique and you cannot add any vertex to $S$ such that the resulting set would form a clique. The set $S$ forms a maximum clique when there is no other set of vertices that forms a clique that is larger than $S$.

You mention bipartite graphs, but the complete $k$-partite graph is not bipartite if $k \geq 3$ (but it is for $k=2$). A bipartite graph contains no triangles, so in such a graph a maximum clique has size (at most) 2, so an efficient algorithm can just return a single edge.

Let $G = K_{n_1,\ldots,n_q}$ for positive integers $n_1,n_2,\ldots,n_q \geq 2$. You can verify that $G$ has maximum clique size $q$, and a total of $n_1 \cdot n_2 \cdots \cdot n_q$ such cliques. An algorithm for enumerating all of them reduces to basic combinatorics (pick one vertex, then how many choices for the remaining vertices do you have when forming a clique?)