  The maximum oriented $k$-forcing number of a simple graph $G$, written
$\MOF_k(G)$, is the maximum directed $k$-forcing number among all orientations
of $G$. This invariant was recently introduced by Caro, Davila and Pepper in
[CaroDavilaPepper], and in the current paper we study the special case where
$G$ is the complete graph with order $n$, denoted $K_n$. While $\MOF_k(G)$ is
an invariant for the underlying simple graph $G$, $\MOF_k(K_n)$ can also be
interpreted as an interesting property for tournaments. Our main results
further focus on the case when $k=1$. These include a lower bound on
$\MOF(K_n)$ of roughly $\frac{3}{4}n$, and for $n\ge 2$, a lower bound of $n -
\frac{2n}{\log_2(n)}$. Along the way, we also consider various lower bounds on
the maximum oriented $k$-forcing number for the closely related complete
$q$-partite graphs.
