  Models of Maximal Flavor Violation (MxFV) in elementary particle physics may
contain at least one new scalar SU$(2)$ doublet field $\Phi_{FV} =
(\eta^0,\eta^+)$ that couples the first and third generation quarks ($q_1,q_3$)
via a Lagrangian term $\mathcal{L}_{FV} = \xi_{13} \Phi_{FV} q_1 q_3$. These
models have a distinctive signature of same-charge top-quark pairs and evade
flavor-changing limits from meson mixing measurements. Data corresponding to 2
fb$^{-1}$ collected by the CDF II detector in $p\bar{p}$ collisions at
$\sqrt{s} = 1.96$ TeV are analyzed for evidence of the MxFV signature. For a
neutral scalar $\eta^0$ with $m_{\eta^0} = 200$ GeV/$c^2$ and coupling
$\xi_{13}=1$, $\sim$ 11 signal events are expected over a background of $2.1
\pm 1.8$ events. Three events are observed in the data, consistent with
background expectations, and limits are set on the coupling $\xi_{13}$ for
$m_{\eta^0} = 180-300$ GeV/$c^2$.
